Glofitamab With Obinutuzumab, Venetoclax, and Lenalidomide for the Treatment of Patients With Newly Diagnosed High Risk Mantle Cell Lymphoma

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Assent, when appropriate, will be obtained per institutional guidelines * Agreement to allow the use of archival tissue from diagnostic tumor biopsies * If unavailable, exceptions may be granted with study principal investigator (PI) approval * Age: \>= 18 to 80 years * Eastern Cooperative Oncology Group =\< 2 * Diagnosis of MCL established by histologic assessment including one of the following: * Immunohistochemistry of the biopsy * Flow cytometry of the biopsy * Evidence of t(11;14) translocation involving the cyclin D1 gene by fluorescence in situ hybridization (FISH), and/or cyclin D1 expression by immunohistochemistry (IHC) unless disease is morphologically consistent with MCL and has IHC expression of SOX11 * Requiring treatment for MCL, and for which no prior systemic anticancer therapies have been received * Local radiotherapy not exceeding a total dose of 20 Gy at least 2 weeks prior the first dose of study therapy is allowed * Laboratory, radiographic, physical exam findings and/or symptoms attributable to MCL * Asymptomatic patients with blastoid or pleomorphic variant can be enrolled * High risk features as classified by Jain et al. * Blastoid/pleomorphic variants * Ki67 \>= 50% * Presence of a TP53 mutation defined by either molecular testing or IHC * del (17p) by FISH * Complex karyotype * High-risk Mantle Cell Lymphoma International Prognostic Index (MIPI) score (\>= 6.2) * Bulky disease * The presence of other high risk gene mutations (KMT2D, NSD2, NOTCH1, CDKN2A, NOTCH2, SMARCA4, CCND1) as long one of the other features above are present * Ability to swallow oral capsules/tablets * Without bone marrow involvement: absolute neutrophil count (ANC) \>= 1,000/mm\^3 With bone marrow involvement: ANC \>= 500/mm\^3 * NOTE: Growth factor is not permitted within 14 days of ANC assessment unless cytopenia is secondary to disease involvement * Without bone marrow involvement: Platelets \>= 75,000/mm\^3 With bone marrow involvement: Platelets \>= 25,000/mm\^3 * NOTE: Platelet transfusions are not permitted within 14 days of platelet assessment unless cytopenia is secondary to disease involvement * Without bone marrow involvement: Hemoglobin \>= 8 g/dL With bone marrow involvement: Hemoglobin \>= 7 g/dL * NOTE: Red Blood cells transfusions are not permitted within 14 days of hemoglobin assessment unless cytopenia is secondary to disease involvement * Total bilirubin =\< 1.5 x upper limit of normal (ULN) (unless has Gilbert's disease) * Aspartate aminotransferase (AST) =\< 3.0 x ULN * Alanine aminotransferase (ALT) =\< 3.0 x ULN * Creatinine clearance of \>= 60 mL/min per 24 hour urine test or the Cockcroft-Gault formula * If not receiving anticoagulants: International normalized ratio (INR) OR prothrombin (PT) =\< 1.5 x ULN If on anticoagulant therapy: PT must be within therapeutic range of intended use of anticoagulants * If not receiving anticoagulants: Activated partial thromboplastin time (aPTT) =\< 1.5 x ULN If on anticoagulant therapy: aPTT must be within therapeutic range of intended use of anticoagulants * Women of childbearing potential (WOCBP): negative serum pregnancy test * Agreement by females and males of childbearing potential to use an effective method of birth control (i.e., failure rate of \< 1% per year) or abstain from heterosexual activity for the course of the study treatment period through at least 30 days after the last dose of venetoclax and lenalidomide, 18 months after the last dose of obinutuzumab, 2 months after the last dose of glofitamab, or 4 months after the last dose of tocilizumab (if applicable) whichever is longer * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only). * All study participants must be registered into the mandatory Revlimid Risk Evaluation and Mitigation Strategy (REMS) (registered trademark) program and be willing and able to comply with the requirements of the REMS (registered trademark) program (including use of aspirin \[ASA\]/ Food and Drug Administration \[FDA\] approved blood thinner) * Females of reproductive potential must adhere to the scheduled pregnancy testing as required in the Revlimid REMS (registered trademark) program Exclusion Criteria: * Treatment with the use of warfarin (because of potential drug-drug interactions that may potentially increase the exposure of warfarin) * Treatment with strong or moderate CYP3A inhibitors or strong CYP3A inducers within 4 weeks or 5 drug-elimination half-lives, whichever is longer, prior to initiation of study drug. Consumed grapefruit, grapefruit products, Seville oranges (including marmalade containing Seville oranges), or star fruit within 3 days prior to first dose of venetoclax * Ongoing corticosteroid use \> 30 mg/day of prednisone or equivalent. Patients who received corticosteroid treatment with =\< 30 mg/day of prednisone or equivalent must be documented to be on a stable dose of at least 4 weeks' duration prior to day 1 of cycle 1. Patients may have received a brief (=\< 7 days) course of systemic steroids (\>= 100 mg prednisone equivalent per day) prior to initiation of study therapy for control of lymphoma-related symptoms * Corticosteroid therapy for control of cancer symptoms is permitted * The use of inhaled corticosteroids is permitted * The use of mineralocorticoids for management of orthostatic hypotension is permitted * The use of physiologic doses of corticosteroids for management of adrenal insufficiency is permitted * Illicit drug or alcohol abuse within 12 months prior to screening, in the investigator's judgment * Prior solid organ transplantation within 60 months and requiring active immunosuppression * Receipt of live-virus vaccine within 28 days prior to the initiation of the study treatment or need for live-virus vaccines at any time during the study treatment * History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agents * History of other malignancy that could affect compliance with the protocol or interpretation of results * Patients with a history of curatively treated basal or squamous cell carcinoma of the skin or in situ carcinoma of the cervix are generally eligible * Patients with low-grade, early-stage prostate cancer (Gleason score 6 or below, stage 1 or 2) with no requirement for therapy at any time prior to study are eligible * Patients with any other malignancy appropriately treated with curative intent and the malignancy has been in remission without treatment for \>= 2 years prior to enrollment are eligible * Patients receiving adjuvant endocrine therapy for non-metastatic, hormone receptor positive breast cancer for \>= 2 years prior to enrollment are eligible * Major surgery (within 4 weeks prior to the start of the first dose of study treatment), other than for diagnosis * Known or suspected chronic active Epstein-Barr viral infection * Known or suspected history of hemophagocytic lymphohistiocytosis (HLH) * Known history of progressive multifocal leukoencephalopathy * Malabsorption syndrome or other condition that precludes enteral route of administration * Known allergy to both xanthine oxidase inhibitors and rasburicase * Positive for hepatitis C virus (HCV) virus by polymerase chain reaction (PCR) at screening. Testing only required if the hepatitis (Hep) C antibody is positive * Positive test results for hepatitis B virus (HBV) infection (defined as positive surface antigen \[HBsAg\]) at screening * Patients with occult or prior HBV infection (defined as negative HBsAg and positive hepatitis B core antibody \[HBcAb\]) may be included if HBV deoxyribonucleic acid (DNA) is undetectable, if they are willing to undergo DNA testing on day 1 of every cycle and every three months for at least 12 months after the last cycle of study treatment and appropriate antiviral therapy * Known active human immunodeficiency virus (HIV) infection. Subjects who have an undetectable or unquantifiable HIV viral load with CD4 \> 200 and are on highly active antiretroviral therapy (HAART) medication are allowed. Testing to be done only in patients suspected of having infections or exposures * Significant or extensive cardiovascular disease such has New York Heart Association class III or IV cardiac disease or Objective Assessment class C or D, myocardial infarction within the last 6 months, unstable arrythmias or unstable angina * Known active bacterial, viral, fungal, mycobacterial, parasitic, or other infection (excluding fungal infections of nail beds) at study enrollment or any major episode of infection (as evaluated by the investigator) within 4 weeks prior to the first study treatment * Suspected or latent tuberculosis (confirmed by positive interferon -gamma release assay) * Females only: Pregnant or breastfeeding or intending to become pregnant during the study or within 18 months after the final dose of all study drugs * Women of childbearing potential must have a negative serum pregnancy test result within 14 days prior to initiation of study drug * History of uncontrolled autoimmune condition or disease requiring active systemic treatment to manage except when on a stable regimen for the treatment of hypothyroidism, Type 1 diabetes mellitus or psoriasis/eczema (topicals only) * Patients with history of immune thrombocytopenic purpura, autoimmune hemolytic anemia, Guillain-Barre syndrome, myasthenia gravis, myositis, rheumatoid arthritis, vasculitis, or other autoimmune disease will be excluded unless they have not required systemic therapy in the last 12 months * Prior treatment with systemic immunosuppressive medications (including, but not limited to, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor agents), within 4 weeks prior to first dose of study treatment * Patients with a history of autoimmune hepatitis, systemic lupus erythematosus, inflammatory bowel disease with active symptoms within last 60 months and on active immunosuppressive therapy, vascular thrombosis associated with antiphospholipid syndrome, Wegener granulomatosis, Sjogren syndrome, multiple sclerosis, or glomerulonephritis will be excluded * Primary or secondary central nervous system (CNS) lymphoma at the time of recruitment or history of CNS lymphoma * Current or history of CNS disease, such as stroke, epilepsy, CNS vasculitis, or neurodegenerative disease * Patients with a history of stroke who have not experienced a stroke or transient ischemic attack within the past 9 months and have no residual neurologic deficits, as judged by the investigator, are allowed * Clinically significant history of cirrhotic liver disease * Any other condition that would, in the investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)