⁃ Patients must have histologically or cytologically confirmed B-cell lymphoma confirmed by the Laboratory of Pathology, NCI, as follows:

• Phase1b

⁃ Aggressive B-cell lymphoma: includes DLBCL and subtypes, transformed lymphoma, Burkitt lymphoma, as well as High-grade B-cell lymphoma with MYC and/or BCL2 and/or BCL6 rearrangement(s).

‣ Indolent B-cell lymphoma:

⁃ CLL/SLL is excluded given alternative dosing of FDA-approved venetoclax for relapsed 17p CLL and increased risk of TLS with CLL/SLL compared to other non-Hodgkin lymphomas.

∙ NOTE: Patients with known active CNS lymphoma are not eligible.

• Phase 2

⁃ Relapsed and/or refractory DLBCL and subtypes, including transformed lymphoma as well as High grade B-cell lymphoma with MYC and/or BCL2 and/or BCL6 rearrangement(s).

⁃ Relapsed and/or refractory Follicular lymphoma (FL)

⁃ Relapsed and/or refractory and untreated Mantle cell lymphoma (MCL)

⁃ Relapsed and/or refractory disease on at least 1 prior treatment regimen, as follows:

∙ Aggressive B-cell lymphoma:relapsed after and/or refractory to at least 1 prior anthracycline-containing regimen

‣ Indolent B-cell lymphoma: relapsed after and/or refractory to at least 1 prior anti-CD20 antibody-containing regimen.

⁃ NOTE: Patients with untreated and relapsed and/or refractory MCL will be included in the phase 2 MCL expansion.

⁃ Patients must have evaluable disease by clinical exam (i.e. palpable lymphadenopathy, measurable skin lesions, etc.), laboratory assessment (i.e. lymphoma involvement of bone marrow or peripheral blood by morphology, cytology or flow cytometry), and/or imaging (measurable lymph nodes or masses on CT or MRI and/or evaluable FDG-avid lesions on PET).

⁃ NOTE: Lesions that have been irradiated cannot be included in the tumor assessment unless unequivocal tumor progression has been documented in these lesions after radiation therapy.

⁃ Age greater than or equal to 18 years

⁃ NOTE: Because no dosing or adverse event data are currently available on the use of venetoclax in combination with ibrutinib, obinutuzumab, prednisone and Revlimid(R) in patients \<18 years of age, children are excluded from this study, but will be eligible for future pediatric trials.

⁃ ECOG performance status less than or equal to 2

⁃ Adequate organ and marrow function as defined below unless dysfunction is secondary to lymphoma:

∙ absolute neutrophil count\* (\*RBC transfusions and use of G-CSF will be allowed in order to meet eligibility parameters): greater than or equal to 1,000/mcL

‣ hemoglobin\* (\*RBC transfusions and use of G-CSF will be allowed in order to meet eligibility parameters): greater than or equal to 8 g/dL

‣ platelets greater than or equal to 75,000/mcL

‣ INR: less than or equal to 1.5 X institutional upper limit of normal (ULN) for patients not receiving therapeutic anticoagulation

‣ PTT/aPTT: less than or equal to 1.5 X institutional ULN normal except if, in the opinion of the investigator, the aPTT is elevated because of a positive Lupus Anticoagulant

‣ Total Bilirubin: less than or equal to 1.5 X institutional ULN (or less than or equal to 3 X institutional ULN for patients with documented Gilberts syndrome)

‣ AST(SGOT)/ALT(SGPT): less than or equal to 2.5 X institutional ULN

‣ Serum Creatinine: less than or equal to 2.0mg/dL OR

‣ Creatinine Clearance: greater than or equal to 60 mL/min/1.73 m\^2 for patients with creatinine levels above 2 mg/dL

• Cr Cl will be calculated with the use of the 24-hour creatinine clearance or modified Cockcroft-Gault equation (eCCR; with the use of ideal body mass \[IBM\] instead of mass):

• (140 - Age) x IBM (kg) x \[0.85 if female\]/ 72 x serum creatinine (mg/dL)

• \*RBC transfusions and use of G-CSF will be allowed in order to meet eligibility parameters.

⁃ Immune-modulating drugs (IMiDs) including Revlimid(R) are known to be teratogenic and potential embryo-fetal harm can be seen with use of venetoclax and ibrutinib. The effects of obinutuzumab on the developing human fetus is unknown. For these reasons, women of child-bearing potential and men must agree to use adequate contraception as described below.

⁃ 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 as outlined below.

‣ Female subjects of childbearing potential (FCBP) must have a negative serum or urine pregnancy test with a sensitivity of at least 25 mIU/mL within 10-14 days and again within 24 hours prior to prescribing Revlimid(R) for Cycle 1 (prescriptions must be filled within 7 days as required by Revlimid REMS(TM) and must either commit to continued abstinence from heterosexual intercourse or begin TWO acceptable methods of birth control, one highly effective method and one additional effective method AT THE SAME TIME, at least 28 days before she starts taking Revlimid(R). FCBP must also agree to ongoing pregnancy testing.

‣ A woman is considered to be of childbearing potential if she is postmenarcheal, has not reached a postmenopausal state (greater than or equal to 12 continuous months of amenorrhea with no identified cause other than menopause), and has not undergone surgical sterilization (removal of ovaries and/or uterus).

‣ Examples of contraceptive methods with a failure rate of less than 1% per year include bilateral tubal ligation, male sterilization, hormonal contraceptives that inhibit ovulation, hormone-releasing intrauterine devices, and copper intrauterine devices.

‣ 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.

⁃ 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 less than 1% per year as noted below. Men must refrain from donating sperm during this same period.

‣ With pregnant female partners, men must remain abstinent or use a condom as noted below 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.

⁃ Contraception Requirements:

• Pre-Treatment/During Treatment:

• -All Drugs- Women- begins 28 days prior to treatment; Men- Begins on day 1

• Post-Treatment:

⁃ Venetoclax- Women- 90 days; Men 90 days

⁃ Ibrutinib- Women- 3 months; Men- 3 months

⁃ Obinutuzumab- Women- 18 months; Men- 6 months

⁃ Revlimid- Women-28 days; Men- 28 days

∙ All study participants must be registered into the mandatory Revlimid REMS(TM) program and be willing and able to comply with the requirements of Revlimid REMS(TM). NOTE: Females of reproductive potential must adhere to the scheduled pregnancy testing as required in the Revlimid REMS(TM) program

‣ Ability of subject to understand and the willingness to sign a written informed consent document.