Inclusion Criteria:

          1. Is able to understand and is willing and able to comply with the study requirements
             and to provide written informed consent.

          2. Documented histologic diagnosis of R/R CLL, RT, or R/R MCL

          3. Safety Lead-In Cohort 1: Patients whose most recent regimen did not include BTK
             inhibitor therapy.

          4. Safety Lead-In Cohort 2: Patients whose most recent regimen did not include Bcl-2
             inhibitor therapy.

          5. Safety Lead-In Cohort 3: APR-246 + venetoclax + rituximab in patients with RT

          6. Prothrombin time (or international normalized ratio) and partial thromboplastin time
             not to exceed 1.2 × the institution's normal range.

          7. Adequate BM function independent of growth factor or transfusion support, per local
             laboratory reference range at screening as follows:

               1. platelet count ≥ 75 000/mm3;

               2. absolute neutrophil count (ANC) ≥ 1000/mm3 unless cytopenia is clearly due to
                  marrow involvement from CLL or MCL

               3. total hemoglobin ≥ 9 g/dL (without transfusion support within 2 weeks of
                  screening);

          8. Adequate organ function as defined by the following laboratory values:

               1. Creatinine clearance ≥ 30 mL/min.

               2. Total serum bilirubin ≤ 1.5 × upper limit of normal (ULN) unless due to Gilbert's
                  syndrome, NHL organ involvement, controlled immune hemolysis or considered an
                  effect of regular blood transfusions.

               3. Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 2.5 × ULN,
                  unless due to NHL organ involvement.

          9. Age ≥18 years at the time of signing the informed consent form.

         10. Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1 or 2.

         11. Projected life expectancy of ≥ 12 weeks.

         12. Women of childbearing potential and men with female partners of childbearing potential
             must be willing to use an effective form of contraception.

             Exclusion Criteria:

         13. Patient with known allergies to xanthine oxidase inhibitors and/or rasburicase.

         14. For patients to receive rituximab on this protocol, prior allergy to rituximab is
             prohibited.

         15. No concomitant anticancer therapies, immunotherapies, cellular, or radiotherapy. No
             major surgery within 3 weeks prior to first dose of study treatment.

         16. Uncontrolled autoimmune hemolytic anemia (AIHA) or immune thrombocytopenia.

         17. Consumption of grapefruit, grapefruit products, Seville oranges, or star fruit within
             7 days of starting study treatment.

         18. Concomitant steroids for disease related pain control are allowed at any dose but must
             be discontinued prior to any study treatment initiation. Chronic use of
             corticosteroids is allowed up to ≤ 20 mg prednisone daily for non-cancer related
             conditions at the time of study start.

         19. History of allogeneic or autologous stem cell transplant (SCT) or CAR-T therapy within
             the last 30 days or with any of the following:

         20. Active graft versus host disease (GVHD)

         21. Cytopenias from incomplete blood cell count recovery post-transplant;

         22. Need for anti-cytokine therapy for residual symptoms of neurotoxicity > grade 1 from
             CAR-T therapy;

         23. Ongoing immunosuppressive therapy.

         24. Known history of human immunodeficiency virus (HIV) serum positivity.

         25. Active hepatitis B/C.

         26. Known central nervous system (CNS) involvement by lymphoma. Patients with previous
             treatment for CNS involvement who are neurologically stable and without evidence of
             disease may be eligible if a compelling clinical rationale is provided to sponsor.

         27. Known neurologic disorder or residual neurologic toxicities that may put patients at
             increased risk of neurologic toxicity in the opinion of the investigator.

         28. Cardiac abnormalities.

         29. Concomitant malignancies or previous malignancies with less than a 1 year disease-
             free interval at the time of signing consent.

         30. A female patient who is pregnant or breast-feeding.

         31. Active uncontrolled systemic infection.

         32. Received an investigational agent within 30 days or within 5 T1/2, whichever is
             shorter prior to the first dose of study treatment.

         33. Clinically significant active malabsorption syndrome or other condition likely to
             affect gastrointestinal (GI) absorption of ibrutinib or venetoclax.

         34. Current treatment with certain strong cytochrome P450 3A4 (CYP3A4) inhibitors or
             inducers and/or strong P-gp inhibitors..