Testing the Addition of a New Anti-cancer Drug, Venetoclax, to Usual Chemotherapy for High Grade B-cell Lymphomas

Inclusion Criteria:

* Pathologic diagnosis of diffuse large B-cell lymphoma (DLBCL) or high grade B-cell lymphoma not otherwise specified (HGBCL not otherwise specified \[NOS\]). Eligible subtypes include DLBCL NOS, Epstein Barr Virus positive (EBV+) DLBCL, HGBCL NOS and DLBCL/HGBCL transformed from an underlying indolent B-cell lymphoma. Patients with T-cell/histiocyte rich large B-cell lymphoma and primary mediastinal B-cell lymphoma are not eligible
* Double hit lymphoma (DHL) or double expressing lymphoma (DEL)

  * DHL is defined as high grade B-cell lymphoma with one of the below:

    * Translocations of MYC and BCL2
    * Translocations of MYC and BCL2 and BCL6 (triple hit lymphoma)
    * Translocations of MYC and BCL6 without BCL2 translocation BUT with immunohistochemistry (IHC) expression of BCL2 (\>=50%)
  * DEL is defined as DLBCL or high grade B-cell lymphoma not otherwise specified (NOS) with protein expression by IHC of both MYC (\>= 40%) and BCL2 (\>= 50%) in the absence of dual translocations of both MYC and BCL2 and/or BCL6). (Double Expressing Lymphoma, DEL). Local determination of fluorescence in situ hybridization (FISH) and IHC will be performed per standardized guidelines and will be acceptable for study entry, but local IHC and FISH results for MYC must be submitted for central review in order to determine eligibility if enrolling as DEL based on local results during phase II. Central pathology review is no longer required as of Update #03.
* The diagnosis of DLBCL/HGBCL and assessment of DEL/DHL will be performed per standardized guidelines at local institutions and patients will be enrolled based on local determination. Cases submitted as DHL must demonstrate the presence of a MYC translocation as well as a translocation of BCL2, BCL6, or both. Cases submitted as a DEL must demonstrate appropriate IHC protein expression of MYC and BCL2, and be negative for translocations of MYC along with translocations of BCL2 and/or BCL6 by FISH. Patients with MYC translocations and no translocations of either BCL2 or BCL6 are eligible for the DEL cohort
* Patients must have FDG-avid disease on PET/CT
* No prior treatment for DLBCL/HGBCL is allowed with the exception of corticosteroids administered for palliation, or a single cycle of either rituximab, cyclophosphamide, doxorubicin, vincristine, and prednisone (R-CHOP) or dose adjusted etoposide, prednisone, vincristine, cyclophosphamide, doxorubicin, and rituximab (DA-EPOCH-R) administered prior to enrollment. Corticosteroids or local radiation therapy are also allowed. Patients may have received intrathecal chemotherapy for CNS prophylaxis prior to registration. This single pre-registration cycle is being allowed to facilitate enrolling patients who required immediate initiation of therapy for rapidly progressing disease, or for patients where FISH or IHC results returned after initiation of chemotherapy rendered them protocol eligible. Patients with DLBCL or HGBCL transformed from an underlying indolent lymphoma cannot have received prior chemotherapy, but prior anti-CD20 monoclonal antibody therapy or radiation therapy for an indolent B-cell lymphoma is allowed.
* Not pregnant and not nursing, because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown.

Therefore, for women of childbearing potential only, a negative pregnancy test done =\< 14 days prior to registration is required.

* Age 18 - 80 years
* Eastern Cooperative Oncology Group (ECOG) Performance Status 0-2.
* Absolute neutrophil count (ANC) \>= 1,000/mm\^3.

  * Unless attributable to lymphoma.
* Platelet count \>= 100,000/mm\^3.

  * Unless attributable to lymphoma.
* Creatinine =\< 1.5 mg/dL OR calculated (calc.) creatinine clearance \>= 50 mL/min.

  * Unless attributable to lymphoma.
* Total bilirubin =\< 2.0 mg/dL.

  * Unless attributable to lymphoma.
  * Unless attributable to Gilbert's disease.
* Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 3 times institution upper limit of normal (ULN).

  * Unless attributable to lymphoma.
* Archival tissue must be available for submission in all patients for histopathology review, though participation in correlative substudies is optional.
* No active ischemic heart disease or congestive heart failure, and left ventricular ejection fraction (LVEF) \>= 45%.
* No known active human immunodeficiency virus (HIV) disease. Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial.
* No known lymphomatous involvement of the central nervous system (CNS). A lumbar puncture or neuroimaging prior to study enrollment is not required in the absence of neurological signs or symptoms concerning for CNS involvement.
* No active hepatitis B or hepatitis C infection. Patients with prior hepatitis B virus (HBV) exposure (positive HBV core antibody and/or surface antigen) are eligible if they have no detectable viral load, and are taking appropriate prophylactic antiviral therapy to prevent reactivation. Patients with history of hepatitis C virus (HCV) are eligible if they have been treated for HCV and have an undetectable HCV viral load.
* Chronic concomitant treatment with strong inhibitors of CYP3A4 is not allowed on this study. Patients on strong CYP3A4 inhibitors must discontinue the drug for 14 days prior to initiation of venetoclax.
* Chronic concomitant treatment with strong CYP3A4 inducers is not allowed. Patients must discontinue the drug 14 days prior to the start of venetoclax.