Testing the Effectiveness of a Combination Targeted Therapy (ViPOR) for Patients With Relapsed and/or Refractory Aggressive B-cell Lymphoma

Inclusion Criteria: * Patient must be ≥ 18 years of age * Patient must have histologically or cytologically confirmed aggressive B-cell lymphoma as follows: * Cohort 1: CD10-negative DLBCL, which includes: * CD10-negative non-GCB DLBCL, not otherwise specified (NOS) (i.e., CD10-/BCL6- or CD10-/BCL6+/MUM1+ DLBCL) * CD10-negative GCB DLBCL, NOS (i.e., CD10-/BCL6+/MUM1- DLBCL) * CD10-negative HGBCL with MYC and BCL6 (without BCL2) translocations (HGBCL-DH-BCL6) * CD10-negative HGBCL, NOS (without MYC and BCL2 translocations) * CD10-negative T-cell/histiocyte-rich large B-cell lymphoma (THRLBCL) OR * Cohort 2: CD10-positive or negative HGBCL with MYC and BCL2 rearrangements (with or without BCL6 rearrangement) (HGBCL-DH-BCL2) * NOTE: The site principal investigator must review and verify the pathology report findings to ensure the patient is eligible and is assigned to the respective cohort at the time of registration * Patient must have relapsed and/or refractory disease after at least 1 prior anthracycline and anti-CD20 antibody-containing regimen * Patient must not have confirmed or suspected primary mediastinal large B-cell lymphoma (PMBL) * Patient must not be pregnant due to the potential harm to an unborn fetus with the treatment regimens being used. * All patients of childbearing potential must have a serum or urine study with a sensitivity of at least 25 mIU/mL within 14 days prior to registration to rule out pregnancy and again within 24 hours prior to starting cycle 1 day 1 of treatment. * A patient of childbearing potential is defined as anyone, regardless of whether they have undergone tubal ligation, who meets the following criteria: 1) has achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy; or 3) has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months) * Patients of childbearing potential must not expect to conceive children by abstaining from sexual intercourse or by using accepted and effective methods of contraception throughout the entire duration of protocol treatment, including during dose interruptions, and for 6 months after the last dose of protocol treatment. Male patients must not father children by abstaining from sexual intercourse or by using a condom during sexual contact with pregnant partners or partners of childbearing potential throughout the entire duration of protocol treatment, including dose interruptions, and for 6 months after the last dose of protocol treatment even if they have had a successful vasectomy * Male patients must agree to not donate semen or sperm during the entire duration of protocol treatment or for at least 28 days after the last dose of lenalidomide * Patient must agree to abstain from breastfeeding during the entire duration of protocol treatment and for at least 6 months after the last dose of protocol treatment * Patient must agree to abstain from donating blood during the entire duration of protocol treatment and for at least 28 days after the last dose of lenalidomide * Patient must have the ability to understand and the willingness to sign a written informed consent document. Patients with impaired decision-making capacity (IDMC) who have a legally authorized representative (LAR) or caregiver and/or family member available will also be considered eligible * Absolute neutrophil count (ANC) ≥ 1,000/mcL without requirement for granulocyte colony stimulating factor (G-CSF) support (obtained ≤ 7 days prior to registration) * Hemoglobin ≥ 8 g/dL (obtained ≤ 7 days prior to registration) * Platelets ≥ 75,000/mcL without requirement for platelet transfusion support (obtained ≤ 7 days prior to registration) * Total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN) (or ≤ 3.0 x institutional ULN for patients with documented Gilberts syndrome) (obtained ≤ 7 days prior to registration) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) ≤ 3.0 x institutional ULN (obtained ≤ 7 days prior to registration) * Creatinine ≤ 1.5 mg/dL OR creatinine clearance ≥ 30 mL/min/1.73 m\^2 (estimated by Cockcroft-Gault method or measured) (obtained ≤ 7 days prior to registration) * Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months of registration are eligible for this trial * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated * Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load * Patient must not have confirmed or suspected primary DLBCL of the central nervous system (CNS) (PCNSL) * Patients with history of secondary CNS lymphoma (SCNSL) are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression * Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial * Patient must not have taken or require warfarin or other strong CYP3A inhibitors or inducers within 7 days prior to registration. * NOTE: Antiplatelet agents, other anticoagulants aside from warfarin, as well as mild or moderate CYP3A inhibitors or inducers are permitted on study but should be used with caution * Patient must not have an uncontrolled intercurrent illness that would interfere with the safety or efficacy assessment of this protocol * Patient must not