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 nerve root involvement)
* Receiving any other treatment which would be considered as a treatment for MCL (with the exception of corticosteroid). If a patient received recent MCL treatment prior to registration, at least 5 half-lives of the drug(s) OR 14 days must have passed following the last dose for the patient to be eligible
* Any of the following medication requirement or recent use:
* Anticoagulation with a vitamin K antagonist =\< 7 days prior to registration
* Requirement of a P-gp inhibitor during the study
* Requirement of a strong cytochrome P450 (CYP) 3A inhibitor or inducer during the study
* Use of a strong or moderate CYP3A inhibitor or inducer =\< 7 days prior to registration
NOTE: Because of their effect on CYP3A4, use of any of the following within 3 days of registration or planned use during study participation is prohibited:
* Grapefruit or grapefruit products
* Seville oranges or products from Seville oranges
* Star fruit
* Human Immunodeficiency Virus (HIV) positive. All subjects will be screened for HIV =\< 14 days prior to registration
* Patient with chronic hepatitis B virus (HBV) or hepatitis C (HCV) requiring treatment. All subjects will be screened for hepatitis B and hepatitis C =\< 14 days prior to registration NOTE: Patients with positive hepatitis B surface antigen (HBsAg) are excluded from participation in this trial. Patients with positive hepatitis B core antibody (anti-HBc) and negative HBsAg require hepatitis B polymerase chain reaction (PCR) evaluation. Patients who are hepatitis B PCR positive will be excluded from participating in this trial NOTE: Patients with positive hepatitis C antibody need to have a negative result for hepatitis C ribonucleic acid (RNA). Patients who are hepatitis C RNA positive will be excluded from participating in this trial
* Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the local investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens
* Uncontrolled intercurrent illness, in the judgement of the local investigator, including, but not limited to:
* New York Heart Association (NYHA) class III or IV or symptomatic congestive heart failure
* Unstable angina or acute coronary syndrome =\< 3 months prior to registration
* Uncontrolled or symptomatic cardiac arrhythmia
* NOTE: Patients with pacemakers are eligible if they have no history of fainting or clinically relevant arrhythmias while using the pacemaker
* Oxygen dependent baseline lung disease (such as interstitial lung disease or chronic obstructive pulmonary disease \[COPD\])
* Ongoing inflammatory bowel disease (such as ulcerative colitis) requiring active treatment
* Ongoing malabsorption syndrome or other condition that precludes enteral route of administration
* Ongoing or active infection (viral, bacterial, or fungal)
* Psychiatric illness/social situations that would limit compliance with study requirements
* History of the following:
* Cerebral vascular accident within 24 weeks prior to registration
* Myocardial infarction within 24 weeks prior to registration
* Major surgery =\< 28 days prior to registration
* Live vaccination =\< 28 days prior to registration
* Life-threatening thrombosis/embolism
* Bleeding diathesis that precludes the use of low-dose aspirin (81 mg daily) or any form of anticoagulation
* Other active primary malignancy (other than localized non-melanotic skin cancer or carcinoma in situ of the cervix) requiring treatment or limiting expected survival to =\< 2 years NOTE: If there is a history of prior malignancy, the patient must be in remission not require ongoing therapy such as radiation, chemotherapy or immunotherapy for their cancer. Patients on adjuvant hormonal therapy for adequately treated nonmetastatic breast or prostate cancer are permitted if they meet other eligibility criteria
* Unable to swallow oral drugs
