Phase 1b/2 Study of Venetoclax, Ibrutinib, Prednisone, Obinutuzumab, and Revlimid (ViPOR) in Relapsed/Refractory B-cell Lymphoma

* INCLUSION CRITERIA: * 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. EXCLUSION CRITERIA: The following restrictions apply to current or prior anti-cancer treatment, prior to the first dose of study drug: * Patients who are actively receiving any other investigational agents. * Any chemotherapy, external beam radiation therapy, or anti-cancer antibodies within 2 weeks prior to the first dose of study drug * Radio- or toxin-immunoconjugates within 10 weeks prior to the first dose of study drug * Previous treatment with greater than one of the study agents (i.e., venetoclax, ibrutinib or Revlimid(R)), excluding prior prednisone or anti-CD20 antibody treatment * Prior allogeneic stem cell (or other organ) transplant within 6 months or any evidence of active graft-versus-host disease or requirement for immunosuppressants within 28 days prior to first dose of study drug * Not recovered (i.e., less than or equal to Grade 1 or baseline) from adverse events due to previously administered anti-cancer treatment, surgery, or procedure. NOTE: Exceptions to this include events not considered to place the subject at unacceptable risk of participation in the opinion of the PI (e.g., alopecia). * Patients requiring the use of warfarin are excluded because of potential drug-drug interactions that may potentially increase the exposure of warfarin. * Patients requiring the following agents within 7 days prior to the first dose of venetoclax are excluded: * Strong CYP3A inhibitors * Strong CYP3A inducers NOTE: Moderate CYP3A inhibitors and inducers should be used with caution and an alternative medication used, whenever possible. Uncontrolled intercurrent illness including, but not limited to the following that may limit interpretation of results or that could increase risk to the patient at the discretion of the investigator: * Symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia * Uncontrolled and/or symptomatic thyroid disease * Known active bacterial, viral, fungal, mycobacterial, parasitic, or other infection (excluding fungal infections of nail beds) at study enrollment, or any major episode of infection requiring treatment with IV antibiotics or hospitalization (relating to the completion of the course of antibiotics) within 2 weeks prior to Cycle 1, Day 1; * Known infection with human T-cell leukemia virus 1 (HTLV-1) * Clinically significant history of liver disease, including viral or other hepatitis, current alcohol abuse, or cirrhosis; as well as active infection with HBV or HCV: --Patients who are positive for HCV antibody must be negative for HCV by polymerase chain reaction (PCR) to be eligible for study participation * Patients with occult or prior HBV infection (defined as positive hepatitis B surface antigen (HBsAg) or positive hepatitis B core antibody (HBcAb) with negative HBsAg) may be included if HBV DNA is undetectable. These patients must be willing to undergo HBV DNA testing during treatment and in surveillance for at least 12 months after completion of study therapy. * Malabsorption syndrome or other condition that precludes enteral route of administration * Psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women, or women who intend to become pregnant during the study, are excluded from this study because Revlimid(R) has known teratogenic effects and venetoclax, ibrutinib and obinutuzumab are agents with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with these agents, breastfeeding should be discontinued if the mother is treated on study. * HIV-positive patients are ineligible because of the potential for pharmacokinetic interactions with venetoclax, ibrutinib and Revlimid(R) and combination antiretroviral therapy. In addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated. * Evidence of active tumor lysis syndrome based on laboratory assessment * History of recent major surgery within 6 weeks prior to the start of Cycle 1, Day 1 other than for diagnosis * History of other active malignancy that could affect compliance with the protocol or interpretation of results * Patients with a history of curatively treated basal or squamous cell carcinoma or stage 1 melanoma of the skin as well as any in situ carcinoma are eligible. * Patients with a malignancy that has been treated with curative intent will also be eligible. Individuals in documented remission without treatment for greater than or equal to 2 years prior to enrollment may be included at the discretion of the investigator. * Known allergy to both xanthine oxidase inhibitors and rasburicase; or, known hypersensitivity to any of the study drugs