Inclusion Criteria

   - Cooperative Oncology Group (ECOG) Performance Status of 0, 1, or 2.

   - Life expectancy >3 months as per investigator's assessment.

   - Part 1 and Part 2 Group 1: Participantts with diffuse large B-cell lymphoma (DLBCL)
   relapsed or refractory to ≥ 1 course of chemotherapy including an anti-CD20 monoclonal
   antibody, and not eligible for autologous stem cell transplantation (ASCT) (including
   due to chemorefractory disease). Participants with transformed FL are eligible,
   provided DLBCL or HGBL-DH/TH histology is biopsy-confirmed prior to study entry and a
   treatment regimen as described above has been administered. The Sponsor retains the
   option to limit the number of participants enrolled with transformed FL.

Part 2, Group 2: Patients identified with DE-DLBCL (expression MYC ≥40%, BCL2 > 50%) and or
HGBL-DH/TH, relapsed or refractory to >= 1 course of chemotherapy including an anti-CD20
monoclonal antibody, and not eligible for ASCT (including due to chemorefractory disease).
Patients with transformed follicular lymphoma (FL) are eligible, provided DE-DLBCL and/or
HGBL-DH/TH histology is biopsy-confirmed prior to study entry and a treatment regimen as
described above has been administered. The Sponsor retains the option to limit the number
of participants enrolled with transformed FL.

   - Part 1 and Part 2: Willing to provide the protocol specified tumor biopsy(ies): at
   screening a fresh biopsy (if no archival biopsy tissue of less than 3 months prior to
   treatment and without intercurrent treatment is available); Part 2: Willing to provide
   an additional biopsy on Cycle 2 Day 15 (+ 2 days).

   - Acceptable liver function, as specified below:

      - Total bilirubin ≤ 2 times upper limit of normal (ULN). (Participants with known
      Gilbert's disease who has serum bilirubin ≤ 3 × ULN may be enrolled).

      - Aspartate transaminase (AST; SGOT), alanine transaminase (ALT; SGPT) ≤ 2.5 × ULN,
      (or ≤ 5 × ULN if tumor involvement (liver) is present).

      - Gamma-glutamyl transferase (GGT) alkaline phosphatase ≤ 2.5 × ULN.

   - Acceptable renal function, as specified below:

   • Creatinine clearance (CrCl) calculated by Cockroft-Gault formula of ≥ 60 mL/min.

   - Acceptable hematologic status (growth factors cannot be used within the previous 7
   days), as specified below:

      - Absolute neutrophil count (ANC) ≥ 1000 cells/μL

      - Hemoglobin ≥ 9 g/dL

      - Platelet count ≥ 75,000 (platelets/μL)

   - Uncontrolled symptomatic hypercalcemia.

   - Acceptable coagulation status, as specified below:

      - Prothrombin time (PT) and partial thromboplastin time (PTT) ≤ 1.2 × ULN (unless
      receiving anticoagulation therapy, if receiving anticoagulation therapy,
      eligibility will be based upon international normalized ratio [INR]).

      - INR ≤ 1.6 (unless receiving anticoagulation therapy).

      - If receiving warfarin: INR ≤ 3.0 and no active bleeding (i.e., no bleeding within
      14 days prior to first dose of study therapy).

   - Acceptable method of contraception

Exclusion Criteria

   - Current central nervous system (CNS) lymphoma or leptomeningeal infiltration.

   - New York Heart Association (NYHA) Class III or IV cardiac disease, myocardial
   infarction, within the past 6 months, unstable arrhythmia, or known pericardial
   disease.

   - Fredericia-corrected QT interval (QTcF) >470 msec (female) or >450 msec (male), or
   history of congenital long QT syndrome.

   - Any electrocardiogram (ECG) abnormality, which in the opinion of the Investigator
   would preclude safe participation in the study.

   - Active, uncontrolled bacterial, viral, or fungal infections, within 7 days of study
   entry requiring systemic therapy.

   - Clinically important respiratory impairment

   - Grade ≥ 3 sensory or motor neuropathy.

   - Any Grade >1 (according to the NCI CTCAE 4.03) adverse reaction unresolved from
   previous treatments and not readily managed and controlled with supportive care.

   - Serious non-malignant disease that could compromise protocol objectives in the opinion
   of the Investigator and/or the Sponsor.

   - History of progressive multifocal leukoencephalopathy (PML).

   - History of other malignancy within 2 years prior to screening, except for ductal
   carcinoma in situ not requiring chemotherapy, appropriately treated carcinoma in situ
   of the cervix, non-melanoma skin carcinoma, low-grade, localized prostate cancer
   (Gleason score ≤ 7) not requiring treatment or appropriately treated Stage I uterine
   cancer.

   - Completion of ASCT within 100 days prior to Day 1 of Cycle1.

   - Prior standard or investigational anti-cancer therapy, as specified below:

      - Radio-immunoconjugate 4 weeks or 5 half-lives, whichever is longer prior to Day 1
      of Cycle 1.

      - Monoclonal antibody or antibody-drug conjugate (ADC) therapy within 3 weeks prior
      to Day 1 of Cycle 1.

      - Radiotherapy, chemotherapy, or targeted small-molecule therapy within 2 weeks
      prior to Day 1 of Cycle 1.

      - CAR T-cell therapy 30 days prior to Day 1 of Cycle 1.

   - History of major solid organ transplant (i.e., heart, lungs, liver and kidney).

   - History of an allogeneic bone marrow transplant.

   - Major surgical procedure within 28 days prior to Day 1 of Cycle 1.

   - Treatment with systemic corticosteroids ≥ 20 mg/day prednisone or equivalent, for
   non-lymphoma treatment reasons. For lower acceptable doses, documentation of a stable
   dose for at least 4 weeks prior to Day 1 of Cycle 1 is required.

   18. Treatment with strong to moderate CYP3A inhibitors or moderate CYP3A inducers
   within 7 days prior to the first dose of study treatment.

   - Treatment with strong CYP3A inducers within 14 days prior to the first dose of study
   treatment of RO6870810/venetoclax.

   - Consumption of grapefruits, grapefruit products, Seville oranges (including marmalade
   that contains Seville oranges), or star fruit within 3 days prior to the first dose of
   venetoclax.

   - Participants who are currently receiving any other investigational agent ((other than
   anti-cancer therapy as specified in exclusion criteria number 13) or have received an
   investigational agent within 30 days or 5 half-lives prior to Day 1 of Cycle 1,
   whichever is longer.

   - Prior treatment with small molecule bromodomain and extra terminal (BET) family
   inhibitor.

   - Known to be human immunodeficiency virus (HIV) positive.

   - Presence of positive test results for hepatitis B surface antigen (HBsAg) or hepatitis
   C antibodies (HcAb) (for participants receiving regimen including rituximab)

   - Pregnant or breastfeeding female.

   - Significant allergy to a biological pharmaceutical therapy that, in the opinion of the
   Investigator, poses an increased risk to the participant.

   - Uncontrolled cancer pain. Participants requiring pain medication must be on a stable
   regimen at study entry. Symptomatic lesions amenable to palliative radiotherapy should
   be treated prior to enrollment.

   - History of severe allergic or anaphylactic reaction to humanized or murine monoclonal
   antibodies (for participants receiving regimen including rituximab).

   - Known sensitivity or allergy to murine products or any component of RO6870810,
   venetoclax, or rituximab.