Golcadomide in Combination With Rituximab for the Treatment of Patients With Relapsed or Refractory Mantle Cell Lymphoma

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Agreement to allow the use of archival tissue from diagnostic tumor biopsies * If unavailable, exceptions may be granted with study principal investigator (PI) approval * Ability to adhere to the study protocol * Age: ≥ 18 years * Eastern Clinical Oncology Group (ECOG) ≤ 2 * Histologically confirmed diagnosis of MCL * Immunohistochemistry of the biopsy * Flow cytometry of the biopsy * Relapsed/ refractory disease * Relapsed/refractory (R/R) MCL after at least one line of therapy including resistant or intolerant to a cBTKi * Fully recovered from the acute toxic effects (except alopecia) to ≤ grade 1 to prior anti-cancer therapy * Ability to swallow pills * Without bone marrow involvement: Absolute neutrophil count (ANC) \> 1.5 × 10\^9/L (ANC \> 1,500/mm\^3) * With bone marrow involvement: ANC \> 1.0 × 10\^9/L (ANC \> 1000/mm\^3) * NOTE: Growth factor is not permitted within 14 days of ANC assessment unless cytopenia is secondary to disease involvement. For patients with significant marrow involvement, eligibility may be confirmed at the discretion of the treating investigator * Without bone marrow involvement: Platelets ≥ 75,000/mm\^3 * With bone marrow involvement: Platelets ≥ 50,000/mm\^3 * NOTE: Platelet transfusions are not permitted within 14 days of platelet assessment unless cytopenia is secondary to disease involvement * Total bilirubin ≤ 1.5 × upper limit of normal (ULN) (≤ 1.5 × ULN if Gilbert's disease) * Aspartate aminotransferase (AST) =\< 2.5 × ULN * Alanine aminotransferase (ALT) ≤ 2.5 × ULN unless elevation is attributable to underlying disease, in which case ALT ≤ 3.0 × ULN * Creatinine clearance of ≥ 30 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 × 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 × ULN. If on anticoagulant therapy: aPTT must be within therapeutic range of intended use of anticoagulants * Seronegative for HIV * Seronegative for hepatitis C virus (HCV), hepatitis B virus (HBV) (surface antigen negative) * Meets other institutional and federal requirements for infectious disease titer requirements * Note Infectious disease testing to be performed within 28 days prior to day 1 of protocol therapy * Woman of childbearing potential must have a negative pregnancy test using a highly sensitive assay (minimum sensitivity 25 IU/L) performed within 10 to 14 days and again within 24 hours prior to receiving the first dose of golcadomide/BMS-986369 * Agreement by females of childbearing potential to use two effective methods of contraception simultaneously without interruption, for at least 28 days before starting study treatment, throughout the entire duration of study treatment, during dose interruptions, and for at least 28 days after the last dose of golcadomide/BMS-986369. The two methods of contraception must include one highly effective method and one additional effective method. Compliance will be documented using the Clinical Trial Pregnancy Risk Awareness Checklist, which must be completed and provided to participants at screening and prior to dispensing of study drug. An individual of childbearing potential (IOCBP) is defined as: * A person who has achieved menarche, has not undergone a documented hysterectomy or bilateral oophorectomy, and has not been naturally postmenopausal for at least 12 consecutive months. Amenorrhea resulting from medical interventions (such as cancer therapy), rather than natural menopause, does not exclude childbearing potential. Criteria: * Achievement of menarche (onset of menstruation). * No history of surgical sterilization: * No documented hysterectomy * No documented bilateral oophorectomy * Not naturally postmenopausal: * Defined as absence of menses for ≥ 12 consecutive months due to natural causes (not due to medical interventions such as chemotherapy, hormonal therapy, or radiotherapy) * Amenorrhea due to medical causes (e.g., cancer therapy, hormonal treatment) does not qualify as natural menopause and does not exclude childbearing potential Exclusion Criteria: * Chemotherapy, radiation therapy (except for palliative radiation therapy \[XRT\]), biological therapy, immunotherapy within 21 days or five half-lives (whichever is shorter for non-radiation therapy) prior to day 1 of protocol therapy * Strong CYP3A4 inducers/ inhibitors within 14 days prior to day 1 of protocol therapy * Herbal medications * History of metastatic cancer * Unstable cardiac disease as defined by one of the following: * Cardiac events such as myocardial infarction (MI) within the past 6 months * New York Heart Association (NYHA) heart failure class III-IV * Uncontrolled atrial fibrillation or hypertension * History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agents * Clinically significant uncontrolled illness * Known seropositive or active infection with HIV, HBV, or HCV * 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 * Females only: Pregnant or breastfeeding * 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)