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 trea