Venetoclax, Ibrutinib, Prednisone, Obinutuzumab, and Revlimid (ViPOR) in Relapsed/Refractory B-cell Lymphoma

Background: B-cell lymphoma is a cancer of white blood cells found in the lymph nodes. It affects the system that fights infections and disease. Researchers want to learn how certain drugs work together to treat B-cell lymphomas. The drugs are venetoclax, ibrutinib, prednisone, obinutuzumab, and lenalidomide (ViPOR). Objective: To study the safety of ViPOR for people with B-cell lymphoma. Eligibility: People ages 18 and older with B-cell lymphoma whose cancer has returned or not improved after treatment Design: Participants will be screened with: * Medical history * Physical exam * Blood, urine, and heart tests * Tissue sample from previous procedure * Imaging scans * Registration for counseling on the risks of lenalidomide. They must get counseling at least every 28 days. Participants will have a bone marrow aspiration before treatment. Participants may have tumor samples taken. Participants will get ViPOR in 21-day cycles. For up to 6 cycles: * Participants will get one drug by IV on days 1 and 2. * Participants will take the other four drugs by mouth on most days. After their first dose of venetoclax, they will stay in the clinic for at least 8 hours and return the next day for monitoring. They may be admitted for more drugs or monitoring. Participants will keep a drug diary. Participants will have a physical exam and blood and urine tests at least once per cycle. They will have scans 4 times over 6 cycles. Participants will have a visit about 1 month after their last dose of study drug. They will then have visits every few months for 3 years, and once a year for years 4 and 5. Visits include a physical exam, blood tests, and scans.

* 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 \