Inclusion Criteria:
* Patients ≥ 18 years of age
* Ability to understand and willingness to sign a written informed consent document
* Patients must have histologic confirmation of mantle cell lymphoma defined by the World Health Organization (WHO) classification and local institutional review
* Participants must have measurable disease, defined as FDG-avid sites on baseline PET/CT measuring 1.5 cm for nodal lesions or 1 cm for extranodal lesions; and/or splenomegaly over 13 cm in largest dimension. Patients with marrow-only mantle cell lymphoma (MCL) are permitted but response assessment requires repeat bone marrow aspirate/biopsy for evaluation
* Participants should have symptomatic disease or indication for treatment according to the treating investigator
* Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2
* Participants of child-bearing potential must be willing to employ two highly effective and acceptable forms of contraception at least 30 days prior to, during, and for at least 90 days after receiving the investigational agents
* Women of childbearing potential (WOCBP) must have a negative serum pregnancy test during screening and must agree to remain abstinent or employ contraceptive methods. Men with female partners who are WOCBP or pregnant must also agree to requirements
* Absolute neutrophil count ≥ 1,000/mm\^3 (independent of growth factor support within 7 days of testing) study entry except in cases of lymphoma involvement of the bone marrow or spleen (in which case absolute neutrophil count \[ANC\] of at least 500/mm\^3 is required)
* Platelets ≥ 75,000/mm\^3 (independent of transfusion support within 7 days of testing) entry except in cases of lymphoma involvement of the bone marrow or spleen (in which case platelet count of at least 50,000/mm\^3 is required)
* Hemoglobin ≥ 8 g/dL (independent of transfusion support within 7 days of testing) except in cases of lymphoma involvement of the bone marrow or spleen
* Total bilirubin \< 1.5 x within normal institutional limits (unless due to Gilbert's disease, or up to 3 x upper limit of normal \[ULN\] if due to lymphoma involvement of liver)
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) ≤ 2.5 x institutional upper limit of normal
* Creatinine clearance ≥ 40 mL/min (as estimated by the Cockcroft-Gault equation, other method including 24-hour urine collection or nuclear medicine renal scan)
Exclusion Criteria:
* Prior systemic therapy for MCL
* Prior radiotherapy is permitted if measurable disease is present outside of radiation field at time of enrollment
* Prephase therapy is permitted and may include steroids (maximum dose 1 mg/kg prednisone equivalent, for up to two weeks) prephase therapy may also be given after consent/during screening
* Participants who are receiving other investigational agents
* Prior solid organ transplantation or prior allogeneic hematopoietic stem cell transplantation
* Prior treatment with a CD20/3 bispecific antibody or polatuzumab
* Positive coronavirus disease of 2019 (COVID-19) test within 7 days of enrollment
* Current grade \> 1 peripheral neuropathy (motor or sensory) by clinical examination or known demyelinating Charcot-Marie-Tooth disease
* Patients with known central nervous system involvement of lymphoma
* History of progressive multifocal leukoencephalopathy (PML)
* Uncontrolled intercurrent illness such as: clinically significant active cardiovascular disease such as uncontrolled or symptomatic arrhythmia, uncontrolled hypertension, congestive heart failure New York Heart Association (NYHA) class III-IV, history of myocardial infarction within 6 months of screening, stroke in last 6 months, liver cirrhosis, or any other serious medical condition, laboratory abnormality, or psychiatric illness that would prevent the subject from signing the informed consent form
* History of prior malignancy that could affect compliance with the protocol or interpretation of results, except for the following:
* Curatively treated basal cell carcinoma or squamous cell carcinoma of the skin or carcinoma in situ of the cervix or breast; or definitely treated, localized prostate cancer
* Early stage prostate cancer with Gleason score 6 or below with no requirement for therapy 4
* Patients in remission with hormone receptor-positive breast cancer on adjuvant endocrine therapy for at least 2 years prior to enrollment
* Other cancers not specified above, that have been curatively treated by surgery and/or radiation therapy from which subject is disease-free for \> 2 years without further treatment
* Known seropositive and requiring anti-viral therapy for human immunodeficiency virus unless controlled on therapy and CD4 count is \> 200/uL during screening
* Has known active hepatitis B (e.g., hepatitis B virus surface antigen \[HbsAg\] reactive or hepatitis B virus \[HBV\] deoxyribonucleic acid \[DNA\] detectable by polymerase chain reaction \[PCR\]) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected), or known chronic active Epstein-Barr virus (EBV)
* History of hemophagocytic lymphohistiocytosis (HLH) or macrophage activation syndrome (MAS)
* Breastfeeding or pregnant women
* Requires chronic treatment with a strong cytochrome P450 3A4 (CYP3A4) inhibitor/inducer. The use of strong CYP3A inhibitors within 1 week or strong CYP3A inducers within 3 weeks of the first dose of study therapy is prohibited
* Known active bacterial, viral, fungal, or other infection that is progressive or uncontrolled at time of screening, or any major episode of infection requiring treatment with IV antibiotics within 4 weeks of day 1 of cycle 1. Grade 1-2 infections treated with oral antibiotic therapy are not necessarily exclusionary, if they are adequately controlled per the treating investigator, and any prescribed antimicrobial therapy is complete before cycle 1 day 1 of treatment
* Administration of a live vaccine within 4 weeks prior to start of study treatment
* Any life-threatening illness, medical condition, or organ system dysfunction that, in the investigator's opinion, could compromise the patient's safety or put the study at risk
* Has difficulty with or is unable to swallow oral medication or has significant gastrointestinal disease that would limit absorption of oral medication
* History of severe bleeding disorder such as hemophilia A, hemophilia B, von Willebrand disease, or history of spontaneous bleeding requiring blood transfusion or other medical intervention
* History of stroke or intracranial hemorrhage within 180 days before first dose of study drug
* Major surgery within 4 weeks of the first dose of study drug
* Current therapy with warfarin or other vitamin K antagonists
* History of autoimmune disease, including but not limited to myocarditis, pneumonitis, myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjögren's syndrome, Guillain-Barré syndrome, multiple sclerosis, vasculitis, or glomerulonephritis
* Patients with a remote history of, or well-controlled autoimmune disease, may be eligible to enroll after discussion with and confirmation by the principal investigator. Patients with controlled Type 1 diabetes mellitus who are on an insulin regimen are eligible for the study
* Patients with a history of autoimmune-related hypothyroidism on a stable dose of thyroid replacement hormone may be eligible for this study
* Patients with a history of disease-related immune thrombocytopenic purpura or autoimmune hemolytic anemia may be eligible for this study
* Patients with eczema, psoriasis, lichen simplex chronicus, or vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis are excluded) are eligible for the study provided all of following conditions are met: Rash must cover \< 10% of body surface area. Disease is well controlled at baseline and requires only low-potency topical corticosteroids. No occurrence of acute exacerbations of the underlying condition requiring psoralen plus ultraviolet A radiation, methotrexate, retinoids, biologic agents, oral calcineurin inhibitors, or high dose steroids within the previous 12 months