Inclusion Criteria:

          -  Relapsed/refractory DLBCL defined as any of the following:

               -  Confirmed DLBCL/Burkitt lymphoma (BL)/B-cell lymphoma, unclassifiable (BCLU) by
                  World Health Organization (WHO) 2016 classification

               -  Double hit lymphoma (DHL) phenotype as confirmed by FISH (fluorescent in-situ
                  hybridization) or IHC (immunohistochemistry)

          -  Relapsed or progression of disease after at least one prior line of standard
             rituximab-cyclophosphamide-hydroxydaunorubicin-oncovin-prednisone (R-CHOP),
             rituximab-etoposide-prednisone-oncovin-cyclophosphamide-hydroxydaunorubicin (R-EPOCH)
             or other R-CHOP-like therapy

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0-2

          -  No prior treatment with a proteasome inhibitor or prior BCL2 inhibitor

          -  No cytotoxic chemotherapy within 2 weeks prior to study treatment

          -  Patients who are not candidates for salvage stem cell transplant or patients who are
             not candidates for CAR-T (chimeric antigen receptor T-cell) therapy, patients who have
             progressed or relapsed after a salvage transplant or CAR-T therapy are eligible

          -  Patients must give informed consent

          -  Prior radiation therapy allowed to < 25% of the bone marrow and patients must have
             recovered from the toxic effects of the treatment prior to study enrollment (except
             for alopecia). Patients treated with standard postoperative adjuvant radiation therapy
             for other cancers are allowed. Prior radiotherapy must be completed 14 days before
             study entry. Lesions that have been radiated in the advanced setting cannot be
             included as sites of measurable disease unless clear tumor progression has been
             documented in these lesions since the end of radiation therapy

          -  Patients with lower blood counts due to marrow involvement by DHL will be eligible for
             the study

          -  Absolute neutrophil count (ANC) >= 1,000/uL

          -  Platelets >= 50,000/uL

          -  Total bilirubin within normal institutional limits

          -  Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase
             [SGOT]/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) <
             3 X institutional upper limit of normal (ULN)

          -  Creatinine < 1.5 the upper limit of normal

        Exclusion Criteria:

          -  Patients who have had prior proteasome inhibitor therapy or prior therapy with
             venetoclax

          -  Patients with known brain metastases will be excluded from this clinical trial because
             of their poor prognosis and because they often develop progressive neurologic
             dysfunction that would confound the evaluation of neurologic and other adverse events

          -  Serious concomitant systemic disorders (including active infections) that would
             compromise the safety of the patient or compromise the patient's ability to complete
             the study, at the discretion of the investigator

          -  Patients with history of hepatitis B with negative viral load are eligible (including
             latent carriers and patient with history of active disease who required treatment)

          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to venetoclax and bortezomib or other agents used in the study

          -  Subjects with human immunodeficiency virus (HIV)/acquired immune deficiency syndrome
             (AIDS) which is not well controlled on antiviral therapy

          -  Patients who have received autologous hematopoietic stem cell transplantation within
             12 months

          -  Subject has received the following within 7 days prior to the first dose of study
             drug: Steroid therapy for anti-neoplastic intent, strong and moderate CYP3A inhibitors
             and/or strong and moderate CYP3A inducers

          -  The effects of combination venetoclax and bortezomib may cause fetal harm. For this
             reason, women of child-bearing potential and men must agree to use adequate
             contraception (hormonal or barrier method of birth control; abstinence) prior to study
             entry, for the duration of study participation and for 12 weeks after. Should a woman
             become pregnant or suspect she is pregnant while participating in this study, she
             should inform her treating physician immediately