PRIMARY OBJECTIVES:
I. To compare the ctDNA clearance proportion (i.e., ctDNA positive \[+\] --\> ctDNA negative \[-\]) at 12 weeks in patients enrolled in Cohort A treated with adjuvant nivolumab versus nivolumab + relatlimab (phase 2 portion).
II. To compare overall survival in patients enrolled in Cohort A treated with adjuvant nivolumab versus nivolumab + relatlimab (phase 3 portion).
III. To compare disease-free survival in patients enrolled in Cohort B randomized to immediate treatment with nivolumab to those randomized to surveillance with subsequent treatment with nivolumab only upon converting to ctDNA(+)
SECONDARY OBJECTIVES:
I. To compare disease-free survival in patients enrolled in Cohort A treated with adjuvant nivolumab versus nivolumab + relatlimab.
II. To define the association between ctDNA clearance and disease-free survival and overall survival for Cohort A patients.
III. To compare overall survival in patients enrolled in Cohort B randomized to immediate treatment with nivolumab to those randomized to surveillance with subsequent treatment with nivolumab only upon converting to ctDNA(+).
IV. To determine the lead time from a ctDNA(+) assay to radiographic recurrence in patients initially ctDNA(-) post-definitive surgery enrolled in Cohort B.
V. To estimate the proportion of Cohort B patients on Arm 4 who become ctDNA(+) and receive nivolumab.
VI. To compare the cumulative incidence of Cohort B patients who become ctDNA(+) between Arms 3 and 4.
VII. To determine the safety of adjuvant nivolumab plus relatlimab.
EXPLORATORY OBJECTIVES:
I. To explore the kinetics of quantitative ctDNA levels (mean number of tumor molecules observed per mL of plasma or MTM/ml) over time and the association between ctDNA kinetics and time-to-event outcomes.
II. To estimate the costs and value of care in patients with a ctDNA(+) assay post-cystectomy treated with adjuvant nivolumab versus nivolumab + relatlimab.
III. To estimate the costs and value of care in patients with a ctDNA(-) assay post-cystectomy treated with adjuvant nivolumab versus surveillance with subsequent treatment with nivolumab at the time of conversion to ctDNA(+).
QUALITY OF LIFE OBJECTIVES:
I. Within each cohort, to compare quality-adjusted survival among randomized arms using European Quality of Life Five Dimension Five Level Scale (EQ-5D-5L).
II. Within Cohort B, to compare overall quality of life (QOL) as measured by the European Organization for the Research and Treatment of Cancer (EORTC) Quality of Life Questionnaire-Core 30 (QLQ-C30) between baseline and 42 months (calculated as the area under the curve) among randomized arms.
III. Within each cohort, to compare overall QOL as measured by the EORTC QLQ-C30 at each time point among randomized arms.
IV. Within each cohort, to compare bladder cancer-specific QOL as measured by the EORTC Bladder Cancer Muscle-Invasive 30 Questionnaire (QLQ-BLM30) at each time point among randomized arms.
V. Within each cohort, to compare patient-reported fatigue as measured by Patient Reported Outcomes Measurement Information System (PROMIS)-Fatigue at each time point among randomized arms.
OUTLINE: Patients are assigned to 1 of 2 cohorts based on ctDNA results.
COHORT A: Patients who are ctDNA(+) are randomized to 1 of 2 arms:
ARM I: Patients receive nivolumab intravenously (IV) over 30 minutes on day 1 of each cycle. Treatment repeats every 28 days for up to 12 cycles in the absence of disease progression or unacceptable toxicity. Patients also undergo collection of tissue during screening and collection of blood throughout the trial. Patients also undergo computed tomography (CT) or magnetic resonance imaging (MRI) scans throughout the trial.
ARM II: Patients receive nivolumab IV over 30 minutes and relatlimab IV over 30 minutes on day 1 of each cycle. Treatment repeats every 28 days for up to 12 cycles in the absence of disease progression or unacceptable toxicity. Patients also undergo collection of tissue during screening and collection of blood throughout the trial. Patients also undergo CT or MRI scans throughout the trial.
COHORT B: Patients who are ctDNA(-) are randomized to 1 of 2 arms:
ARM III: Patients receive nivolumab IV over 30 minutes on day 1 of each cycle. Treatment repeats every 28 days for up to 12 cycles in the absence of disease progression or unacceptable toxicity. Patients also undergo collection of tissue during screening and collection of blood throughout the trial. Patients also undergo CT or MRI scans throughout the trial.
ARM IV: Patients undergo ctDNA surveillance consisting of collection of tissue and blood during screening and collection of blood only on study and during follow up. Patients who convert to ctDNA(+) during surveillance then receive nivolumab IV over 30 minutes and relatlimab IV over 30 minutes on day 1 of each cycle. Treatment repeats every 28 days for up to 12 cycles in the absence of disease progression or unacceptable toxicity. Patients also undergo CT or MRI scans throughout the trial.
After completion of study treatment, patients are followed up at weeks 60, 72, 84, 96, 120, 144, 196, and 248.
Inclusion Criteria:
* PRE-REGISTRATION: Histologically confirmed muscle-invasive urothelial carcinoma of the bladder. Variant histology, including neuroendocrine differentiation, is allowed if urothelial cancer is predominant histology (any amount of squamous differentiation is allowed provided the tumor is not a pure squamous cell cancer)
* PRE-REGISTRATION: Patient must have had radical cystectomy and lymph node dissection \>= 3 weeks, but =\< 12 weeks prior to pre-registration. Patients who have had a partial cystectomy as definitive therapy are not eligible
* PRE-REGISTRATION: No gross cancer at the surgical margins. Microscopic invasive urothelial carcinoma at the surgical margins (i.e., "positive margins") are allowed. Carcinoma in situ (CIS) at margins is considered negative margins
* PRE-REGISTRATION: No evidence of residual cancer or metastasis after cystectomy (imaging is not required prior to pre-registration but is required prior to registration)
* PRE-REGISTRATION: Have undergone a radical cystectomy with pathological evidence of urothelial carcinoma of the bladder at high risk of recurrence as described in one of the two scenarios below (i or ii). The 7th edition of American Joint Committee on Cancer (AJCC) staging will be utilized.:
* (i) Patients who have not received neoadjuvant cisplatin-based chemotherapy: pT3-pT4\* or pT0/x-pT4/N+ on cystectomy and are not eligible for adjuvant cisplatin chemotherapy
* (i) Patients ineligible for cisplatin due to at least one of the following criteria and reason for ineligibility should be documented:
* (i) Creatinine Clearance (using Cockcroft-Gault): \< 60 mL/min
* (i) Common Terminology Criteria for Adverse Events (CTCAE) version 5, grade \>= 2 audiometric hearing loss
* (i) CTCAE version 5, grade \>= 2 or above peripheral neuropathy
* New York Heart Association Class III heart failure
* (i) Eastern Cooperative Oncology Group (ECOG) performance status = 2
* (i) Patients who are eligible for cisplatin may be candidates if they refuse available adjuvant chemotherapy, despite being informed by the investigator about the treatment options. The patient's refusal must be documented.
* (i) Patients with pT2N0 urothelial cancer on cystectomy (without prior neoadjuvant chemotherapy) with ctDNA(+) Signatera results based on an assay performed post-cystectomy as part of routine care outside of the study may proceed with pre-registration but require confirmation of ctDNA(+) Signatera testing on repeat "central testing" in the context of A032103 testing. Patients with pT2N0 with central testing not confirming ctDNA(+) will not be eligible for A032103 (Note: this is distinct from patients with ypT2N0 who are eligible based on ii).
* (ii) Patients who received cisplatin-based neoadjuvant chemotherapy: ypT2-ypT4 or ypT0/x-pT4/N+ on cystectomy
* PRE-REGISTRATION: Available tumor tissue for central Signatera testing to be submitted after pre-registration. Central testing is defined as testing performed as part of the A032103 study prior to registration and is provided by the study and not routine standard commercial testing. Patients who have already had Signatera testing performed as part of routine care will require repeat central testing as part of the A032103 study to be eligible for registration/randomization. Tumor tissue from the cystectomy is preferred over tissue from prior transurethral resection
* PRE-REGISTRATION: Age \>= 18 years
* PRE-REGISTRATION: ECOG Performance Status 0-2
* PRE-REGISTRATION: Not pregnant and not nursing, because this study involves an agent that has known genotoxic, mutagenic and teratogenic effects
* PRE-REGISTRATION: No postoperative/adjuvant systemic therapy after cystectomy
* PRE-REGISTRATION: No adjuvant radiation after cystectomy
* PRE-REGISTRATION: No treatment with any other type of investigational agent =\< 4 weeks before pre-registration
* PRE-REGISTRATION: Not have ever received prior treatment with PD-1/PD-L1 blockade.
* PRE-REGISTRATION: Not have ever received prior treatment with LAG-3 blockade.
* PRE-REGISTRATION: Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial
* PRE-REGISTRATION: Absolute Neutrophil Count (ANC) \>= 1,200/mm\^3
* PRE-REGISTRATION: Platelet count \>= 100,000/mm\^3
* PRE-REGISTRATION: Hemoglobin \>= 8 g/dL
* PRE-REGISTRATION: Creatinine =\< 1.5 x upper limit of normal (ULN) or calculated (calc.) creatinine clearance \> 30 mL/min (using either Cockcroft-Gault formula or Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation
* PRE-REGISTRATION: Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 3 x ULN
* PRE-REGISTRATION: Total bilirubin =\< 1.5 x upper limit of normal (ULN) (except in patients with Gilbert Syndrome, who can have total bilirubin \< 3.0 mg/dL)
* PRE-REGISTRATION: For women of childbearing potential only: A negative urine or serum pregnancy test done =\< 14 days prior to pre-registration is required
* PRE-REGISTRATION: Not currently requiring hemodialysis
* PRE-REGISTRATION: No current or prior history of myocarditis
* PRE-REGISTRATION: No active autoimmune disease or history of autoimmune disease that might recur, which may affect vital organ function or require immune suppressive treatment including systemic corticosteroids. These include but are not limited to patients with a history of immune related neurologic disease, multiple sclerosis, autoimmune (demyelinating) neuropathy, Guillain-Barre syndrome, myasthenia gravis; systemic autoimmune disease such as systemic lupus erythematosus (SLE), connective tissue diseases, scleroderma, inflammatory bowel disease (IBD), Crohn's, ulcerative colitis, hepatitis; and patients with a history of toxic epidermal necrolysis (TEN), Stevens- Johnson syndrome, or phospholipid syndrome because of the risk of recurrence or exacerbation of disease.
* PRE-REGISTRATION: Patients with vitiligo, endocrine deficiencies including type I diabetes mellitus, thyroiditis managed with replacement hormones including physiologic corticosteroids are eligible.
* PRE-REGISTRATION: Patients with rheumatoid arthritis and other arthropathies, Sjögren's syndrome and psoriasis controlled with topical medication and patients with positive serology, such as antinuclear antibodies (ANA), anti-thyroid antibodies should be evaluated for the presence of target organ involvement and potential need for systemic treatment but should otherwise be eligible.
* PRE-REGISTRATION: No current pneumonitis or prior history of non-infectious pneumonitis that required steroids within the previous 5 years.
* PRE-REGISTRATION: No known active hepatitis B (e.g., hepatitis B surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected).
* PRE-REGISTRATION: For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load.
* PRE-REGISTRATION: Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible.
* PRE-REGISTRATION: No concurrent antineoplastic therapy.
* PRE-REGISTRATION: No current immunosuppressive agents (with the exception of corticosteroids as described below).
* PRE-REGISTRATION: No condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of pre-registration (with the exception of steroid pre-medications for contrast allergies). Inhaled or topical steroids and adrenal replacement doses \< 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease.
* REGISTRATION: Patient must have had radical cystectomy and lymph node dissection =\< 18 weeks prior to registration.
* REGISTRATION: Must have evaluable ctDNA Signatera assay result (i.e., ctDNA\[+\]or ctDNA\[-\]) based on test performed as part of central testing after pre-registration to A032103. Central testing is defined as testing performed as part of the A032103. Local/commercial testing results may not be used for registration to A032103
* Cisplatin-ineligible (or cisplatin-declining) patients with a pT2N0 urothelial cancer on cystectomy who were pre-registered based on routine standard care ctDNA(+) Signatera testing must have confirmed ctDNA(+) Signatera testing on central testing. If central Signatera testing yields a ctDNA(-) result, these patients are ineligible. NOTE: This is a distinct consideration from patients with ypT2-4 and/or ypN+ urothelial cancer (i.e., patients who had received neoadjuvant cisplatin-based chemotherapy) who are eligible with either ctDNA(+) or ctDNA(-) central Signatera testing
* REGISTRATION: All patients must have confirmed disease-free status defined as no measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1, or definitive non-measurable radiographic metastatic disease, within 60 days prior to registration. Patients with equivocal nodes less than 15 mm in short axis, or \< 10 mm in long axis for non-lymph node lesions, not considered by the investigator to represent malignant disease will be eligible. Attempts should be made to resolve the etiology of equivocal lesions with complementary imaging (e.g., PET scan) or biopsy.
* REGISTRATION: No major surgery =\< 3 weeks before registration.
* REGISTRATION: No live vaccine within 30 days prior to registration. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette- Guerin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g., FluMist \[registered trademark\]) are live attenuated vaccines and are not allowed. Coronavirus disease 2019 (COVID-19) vaccines are not live vaccines and are allowed
* COHORT B, ARM 4 PATIENTS INITIATING NIVOLUMAB AFTER CONVERSION OF ctDNA ASSAY FROM ctDNA(-) to ctDNA (+):
* Patient must have converted to ctDNA(+) during serial monitoring performed centrally in the setting of the A032103 study
* COHORT B, ARM 4 PATIENTS INITIATING NIVOLUMAB AFTER CONVERSION OF ctDNA ASSAY FROM ctDNA(-) to ctDNA (+):
* No evidence of metastatic disease on the most recent scheduled imaging assessment as outlined in the study calendar (no repeat imaging is necessary specifically at the time of the conversion from ctDNA\[-\] to ctDNA\[+\]).
* COHORT B, ARM 4 PATIENTS INITIATING NIVOLUMAB AFTER CONVERSION OF ctDNA ASSAY FROM ctDNA(-) to ctDNA (+):
* No change in clinical condition and/or laboratory tests that would impact the safety of nivolumab in the opinion of the treating investigator
* COHORT B, ARM 4 PATIENTS INITIATING NIVOLUMAB AFTER CONVERSION OF ctDNA ASSAY FROM ctDNA(-) to ctDNA (+):
* =\< 6 weeks from reporting of ctDNA(+) result by Natera.
