Tafasitamab, Lenalidomide and Venetoclax for the Treatment of Relapsed or Refractory Mantle Cell Lymphoma

Inclusion Criteria: * Age \>= 18 years old * Confirmed pathology diagnosis of mantle cell lymphoma (MCL) with t(11;14)(q13;q32) translocation or cyclin D1 overexpression NOTE: Patients with relapsed/refractory MCL after prior anti-CD19 therapy (such as chimeric antigen receptor \[CAR\] T-cell therapy) should have confirmed preserved expression of CD19, unless a biopsy is not feasible or associated with a high risk of complications in the treating physician's opinion * Relapsed or refractory disease, which is defined as patients with \>= 1 line of prior systemic treatment NOTE: Prior exposure to lenalidomide or venetoclax is allowed, provided there was no disease progression on lenalidomide or venetoclax * In the view of the treating physician, the patient is in need of treatment, for example, with lymphoma-related symptoms or cytopenia * Evaluable disease, which is defined as at least one lymph node or other type of lesion that has a size \>= 1.5 cm, or spleen size \>= 15 cm or white blood cell (WBC) \>= 30,000/mm\^3 in leukemic non-nodal MCL patients * Eastern Cooperative Oncology Group Performance Status (PS) 0, 1, or 2 * Absolute neutrophil count (ANC) \>= 1500/mm\^3 (obtained =\< 14 days prior to registration) * Platelet count \>= 75,000/mm\^3 (\>= 50,000/mm\^3 if there is evidence of bone marrow involvement by MCL or hypersplenism) (obtained =\< 14 days prior to registration) * Hemoglobin \> 8.0 g/dL (obtained =\< 14 days prior to registration) * Activated partial thromboplastin time (aPTT) or partial thromboplastin time (PTT) =\< 1.5 × upper normal limit (ULN) (obtained =\< 14 days prior to registration) * Prothrombin (PT) or international normalized ratio (INR) =\< 1.5 × upper normal limit (ULN) (obtained =\< 14 days prior to registration) * Total bilirubin =\< 1.5 × ULN (or =\< 3 × ULN if there is evidence of parenchymal liver involvement with MCL or documented Gilbert's disease) (obtained =\< 14 days prior to registration) * Alanine aminotransferase (ALT) and aspartate transaminase (AST) =\< 3 × ULN (or =\< 5 × ULN if there is evidence of parenchymal liver involvement with MCL) (obtained =\< 14 days prior to registration) * Calculated creatinine clearance \> 60 ml/min using the Cockcroft-Gault formula (obtained =\< 14 days prior to registration) * Negative pregnancy test done =\< 7 days prior to registration, for women of reproductive potential only NOTE: If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required NOTE: Females of reproductive potential include all females who are menstruating, amenorrheic from previous medical treatments, under 50 years of age, and/or perimenopausal, and do not qualify for the females not of reproductive potential category. Females not of reproductive potential include females who have been in natural menopause for at least 24 consecutive months, or who have had a hysterectomy and/or bilateral oophorectomy, or female children who have not started menstruating * Agree to use effective contraception during study treatment and for 4 weeks after last dose of lenalidomide and for 3 months after last dose of tafasitamab (whichever is longer) Females of reproductive potential must commit either to abstain continuously from heterosexual sexual intercourse or to use two methods of reliable birth control simultaneously: one highly effective form of contraception - tubal ligation, intrauterine device (IUD), hormonal (birth control pills, injections, hormonal patches, vaginal rings, or implants), or partner's vasectomy, and one additional effective contraceptive method - male latex or synthetic condom, diaphragm, or cervical cap. Contraception should continue during therapy, during dose interruptions, and for 4 weeks following discontinuation of lenalidomide and for 3 months after discontinuation of tafasitamab (whichever is longer). Reliable contraception is indicated even where there has been a history of infertility, unless due to hysterectomy. If needed, females of reproductive potential should be referred to a qualified provider of contraceptive methods Males must always use a latex or synthetic condom during any sexual contact with females of reproductive potential during trial therapy, during dose interruptions, and for 4 weeks following discontinuation of lenalidomide and for 3 months after discontinuation of tafasitamab (whichever is longer), even if they have undergone a successful vasectomy. Male patients must not donate sperm * Willing to be registered into the mandatory REVLIMID REMS (trademark) program, and willing and able to comply with the requirements of the REVLIMID REMS program * Able to take low-dose aspirin (81 mg) daily or an alternative form of anticoagulation * Subject must voluntarily sign and date an informed consent =\< 28 days prior to registration * Willing to return to enrolling institution for follow-up during the active monitoring phase (i.e., active treatment and clinical follow-up) of the study * Willing to provide mandatory blood specimens for correlative research and banking for future correlative research pertinent to this study Exclusion Criteria: * Any of the following: * Pregnant persons * Nursing persons (lactating persons are eligible provided that they agree not to use their breast milk to feed while receiving treatment on the study or within 3 months of the last dose of study treatment) * Men or women of reproductive potential who are unwilling to employ adequate contraception during treatment and for 4 weeks after last dose of lenalidomide or for 3 months after last dose of tafasitamab (whichever is longer) * Any of the following prior therapies: * Autologous stem cell transplant =\< 90 days prior to registration * Allogeneic stem cell transplant * Anti-CD19 CAR T-cell therapy =\< 90 days prior to registration * Any central nervous system (CNS) involvement by MCL (e.g., any parenchymal, leptomeningeal, cerebrospinal fluid \[CSF\], cranial or spinal