Inclusion Criteria:

          -  Patients must have histologically confirmed (biopsy-proven) diagnosis of mantle cell
             lymphoma (MCL), with documented cyclin D1 (BCL1) expression by immunohistochemical
             stains and/or t(11;14) by cytogenetics or FISH.

          -  Patients must have measurable or evaluable disease as defined as a lymph node
             measuring >1.5 cm in any dimension or splenomegaly with spleen >15 cm in craniocaudal
             dimension.

          -  Age ≥ 60 years.

          -  No intention to undergo consolidation with high dose chemotherapy and autologous stem
             cell rescue (Autologous Stem Cell Transplant) in first remission.

          -  ECOG performance status of 0-2.

          -  Ability to understand and willingness to sign Institutional Review Board
             (IRB)-approved informed consent.

          -  Willing to provide mandatory tissue samples (if sufficient tissue available), bone
             marrow and blood samples for research purposes.

          -  Adequate organ function as measured by the following criteria, obtained ≤ 2 weeks
             prior to registration:

               -  Absolute Neutrophil Count (ANC) ≥ 1000/mm³

               -  Hemoglobin ≥ 8 g/dL

               -  Platelets ˃75,000/mm³

               -  Creatinine clearance ≥ 40 mL/min, calculated with the use of 24-hour creatinine
                  clearance or by Cockcroft-Gault formula

               -  Total Bilirubin ≤ 1.5x Upper Limit of Normal (ULN) or ≤ 3x ULN for patients with
                  documented Gilbert's syndrome

               -  Aspartate aminotransferase (AST)/ alanine aminotransferase (ALT) ≤ 2.5x ULN

          -  All females of childbearing potential (not surgically sterilized and between menarche
             and 1 year post menopause) must have a blood test to rule out pregnancy within 2 weeks
             prior to registration.

          -  Women must not be pregnant or breastfeeding. Females of childbearing potential who are
             sexually active with a non-sterilized male partner and sexually active men must agree
             to use 2 methods of adequate contraception (hormonal plus barrier or 2 barrier forms)
             prior to study entry, for the duration of study participation, and for 12 months after
             last dose of therapy. Method of contraception must be documented.

          -  Patients should not have prior chemotherapy, radiotherapy or immunotherapy for
             lymphoma.

          -  Patients must have no recent (<1 year) history of malignancy except for the following:

               -  adequately treated non-melanoma skin cancer

               -  adequately treated Stage I melanoma of the skin

               -  in situ cervical cancer

               -  low grade prostate adenocarcinoma (Gleason grade ≤ 6) managed with observation
                  and stable for 6 months.

          -  Patients should not have known evidence of central nervous system (CNS) lymphoma.

          -  Patients must not have received a prior allogeneic stem cell transplant or solid organ
             transplant (except for cornea) for any indication.

          -  Patients must have no active, uncontrolled infections.

          -  Patients must not have active hepatitis B or be chronic carriers of hepatitis B. This
             is defined as patients with hepatitis B surface antigen (HBsAg) positive. Patients
             with prior exposure to hepatitis B (hepatitis B core antibody (anti-HBc) positive AND
             HBsAg negative) are allowed with a protective level hepatitis B surface antibody AND a
             negative hepatitis B viral load by polymerase-chain reaction (PCR).

          -  Patients must not have active hepatitis C (HCV) as defined by a hepatitis C viral load
             detectable by PCR. Patients with a negative HCV antibody are assumed to have a
             negative HCV viral load. Patients with a positive HCV antibody must have a negative
             hepatitis C viral load by PCR. Prior treatment for an active HCV infection will be
             allowed as long as the hepatitis C viral load by PCR is negative.

          -  Patients must not have known active Human Immunodeficiency Virus (HIV). Testing not
             required in absence of clinical suspicion.

          -  Patients must not have evidence of significant, uncontrolled concomitant diseases,
             including psychiatric diseases, that could affect compliance with the protocol or
             interpretation of results or that could increase risk to the patient.

          -  Patients must not have conditions that preclude oral administration or absorption of
             medications through the GI tract, including but not limited to the inability to
             swallow pills or malabsorption syndromes.

          -  Patients must not have known allergies to both xanthine oxidase inhibitors and
             rasburicase.

          -  Patients must not require the use of warfarin. Blood thinners of other classes are
             permitted.

          -  Patient may not receive the following agents within 7 days prior to the first dose of
             venetoclax:

               -  Strong and moderate CYP3A inhibitors

               -  Strong and moderate CYP3A inducers

               -  Strong and moderate P-gp inhibitors

          -  Patients must not have consumed grapefruit, grapefruit products, Seville oranges
             (including marmalade containing Seville oranges), or star fruit within 3 days prior to
             the first dose of venetoclax.