The Study of Bendamustine, Rituximab, Ibrutinib, and Venetoclax in Relapsed, Refractory Mantle Cell Lymphoma

Inclusion Criteria: * Age greater than or equal to 18 years * Histologically confirmed MCL * Relapse, refractory or progressive disease following at least 1 line of systemic therapy for mantle cell lymphoma * ECOG Performance Status \</= 2 * Patients must have completed anticancer treatment with chemotherapy, small molecule inhibitors, immune modulator drugs, biologics, and/or treatment with other anticancer agents at least 3 weeks prior treatment, or 2 weeks if progressing, and recovered from clinically significant toxicity associated with treatment ° Palliative radiotherapy must have been discontinued at least 1 week prior to treatment in this study * Short-course corticosteroids are allowed (≤ 10 days) and must be discontinued prior to study treatment start (Cycle 1, Day 1) ° Ongoing administration of a stable dose of corticosteroid therapy (equivalent to ≤ 30 mg prednisone daily and previously received for ≥ 30 days) is permissible provided there is evidence of measurable disease and there will be no increase in steroid dose during the clinical trial * Patients who have been previously treated with BR or Bendamustine alone are eligible, provided they did not progress during treatment or within 6 months of completing BR or B treatment * Patients who have been previously treated with ibrutinib or acalabrutinib (or any alternate BTK-inhibitor) are eligible, provided they had evidence of response (at least Stable Disease, Partial Response, or Complete Response) and did not progress within 6 months of treatment initiation * Female subject of childbearing potential should have a negative urine or serum pregnancy within 2 weeks prior to receiving the first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. * A positive serum pregnancy test due to fertility preservation will not be an exclusion after physician review * Adequate organ function and laboratory values within the following ranges: * Absolute neutrophil count \> 1,000 cells/mm3 (1.0 x 109L), if neutropenia is due to bone marrow involvement absolute neutrophil count must be \>/= 500 cells.mm3 (0.5 x 10\^9/L) * Platelet count \> 75,000 cells/mm3 (75 x 109/L), unless thrombocytopenia is due to bone marrow involvement platelet count must be greater than 25,000 cells/mm3 * Hemoglobin \> 8.0 g/dL * Serum aspartate transaminase (AST) and alanine transaminase (ALT) \</= 2.5 x upper limit of normal (ULN) * Estimate creatinine clearance (Cockcroft-Gault) \>/= 40 mL/min. If creatinine clearance is \< 40 mL/min, but the serum creatinine is within institutional normal limits, the patient will be eligible * Bilirubin \<1.5 x ULN (unless bilirubin rise is due to Gilbert's syndrome or of non-hepatic origin) * For women of childbearing potential: * Agreement to remain abstinent (refrain from heterosexual intercourse) or use a contraceptive method with a failure rate of \< 1% per year during the treatment period and for at least 30 days afte rthe last dose of venetoclax or 18 months after the last dose of rituximab, whichever is longer * Examples of contraceptive methods with a failure rate of \< 1% per years include bilateral tubal ligation, male sterilization, hormonal contraceptives that inhibit ovulation, hormone-releasing intrauterine devices, and copper intrauterine devices * A woman is considered to be of childbearing potential if she is postmenarcheal, has not reached a postmenopausal state (\>/= 12 continuous months of amenorrhea with no identified cause other than menopause), and has not undergone surgical sterilization (removal of ovaries and/or uterus) * For men: * Agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive measures, and agreement to refrain from donating sperm, as defined below * With female partners of childbearing potential, men must remain abstinent or use a condom plus an additional contraceptive method that together result in a failure rate of \<1% per year during the treatment period and for at least 6 months after the last dose of rituximab. Men must refrain from donating sperm during this same period. * With pregnant female partners, men must remain abstinent or use a condom during the treatment period and for at least 6 months after the last dose of rituximab to avoid exposing the embryo * The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the patient. Periodic abstinence (e.g. calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not acceptable methods of contraception Exclusion Criteria: * Prior therapy with venetoclax or alternate BCL-2 inhibitor * Any life-threatening illness, medical condition, or organ system dysfunction that, in the opinion of the investigator, could compromise the subject's safety or put the study outcomes at undue risk. * Unable to swallow capsules or tablets, malabsorption syndrome, disease significantly affecting gastrointestinal function, resection of the stomach or small bowel, symptomatic inflammatory bowel disease or ulcerative colitis, or partial or complete bowel obstruction or other condition that precludes enteral route of administration * Cerebral/meningeal disease related to the underlying malignancy. Patients with a history of cerebral/meningeal disease related to the underlying malignancy are allowed if prior central nervous system disease has been definitively treated with no evidence of disease or requirement for steroids * Active HIV or hepatitis B or C with positive viral load, requiring anti-viral therapy * Bleeding diathesis or use of warfarin or other vitamin K antagonist * Prior history of infusion reactions or hypersensitivity to any of the study drugs * Active concurrent malignancy requiring active therapy * Pregnant or lactating females * Prior autologous stem cell transplant within 90 days of study start * Prior allogenic stem cell transplant within 12 months of study start * Patients with active graft-versus-host-disease are not eligible * Patients receiving immunosuppressive therapy for prevention of graft-versus-host-disease are not eligible * Patients who requires treatment with a potent cytochrome P450 (CYP) 3A inhibitor or inducer * 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 requiring treatment with IV antibiotics or hospitalization (relating to the completion of the course of antibiotics) within 2 weeks prior to Cycle 1, Day 1 * Clinically significant history of liver disease, including viral or other hepatitis, current alcohol abuse, or cirrhosis * Receipt of live-virus vaccines within 28 days prior to the initiation of study treatment or need for live-virus vaccines at any time during study treatment