Testing CC-486 (Oral Azacitidine) Plus the Standard Drug Therapy in Patients 75 Years or Older With Newly Diagnosed Diffuse Large B Cell Lymphoma

Inclusion Criteria:

* Participants must have histologically or cytologically confirmed diffuse large B-cell lymphoma (DLBCL), Ann Arbor Stage IIX (bulky), III or IV. Participants with DLBCL transformed from follicular lymphoma (FL) or marginal zone lymphoma (MZL, including mucosa-associated lymphoid tissue \[MALT\] lymphomas), lymphoplasmacytic lymphoma (LPL), or nodular lymphocyte-predominant Hodgkin Lymphoma (NLPHL) are eligible. Participants with Grade IIIB follicular lymphoma (FL) or high-grade B-cell lymphomas with MYC and BCL2 and/or BCL6 rearrangements are also eligible. Participants with DLBCL that arose from prior CLL (Richter's transformation) are not eligible.
* As defined by the World Health Organization (WHO), eligible lymphoma subtypes include the following:

* DLBCL, not otherwise specified (NOS)
* DLBCL, germinal-center B-cell type (GCB)
* DLBCL, activated B-cell type (ABC)
* T-cell histiocyte-rich B-cell lymphomas (THRBCL)
* Primary cutaneous DLBCL, leg type
* Intravascular large B cell lymphoma
* EBV+ DLBCL, NOS
* DLBCL associated with chronic inflammation
* HHV8+ DLBCL, NOS
* High-grade B-cell lymphoma with MYC and BCL2 and/or BCL6 rearrangements
* High grade B-cell lymphoma, NOS
* Follicular lymphoma grade 3b
* Participants must have staging imaging performed within 28 days prior to registration, as follows. Positron emission tomography (PET)-computed tomography (CT) baseline scans are strongly preferred; diagnostic quality magnetic resonance imaging (MRI), contrast-enhanced CT, or contrast-enhanced MRI scans are also acceptable if PET-CT is not feasible at baseline. Note: PET-CT will be required at end of treatment (EOT) and progression for response assessment. Participants must have measurable disease (at least one lesion with longest diameter ≥ 1.5 cm). All measurable lesions (longest diameter \>= 1.5 cm) must be assessed within 28 days prior to registration. Tests to assess non-measurable disease must be performed within 42 days prior to registration.
* Participants with known human immunodeficiency virus (HIV)-infection are eligible providing they are on effective anti-retroviral therapy and have undetectable viral load at their most recent viral load test (must be within 26 weeks prior to registration). Participants with known HIV must have a CD4 count checked within 28 days prior to registration, but may proceed with therapy regardless of CD4 count.
* All participants must be screened for chronic hepatitis B virus (HBV) within 28 days prior to registration. Participants with known HBV infection (positive serology) must also have a HBV viral load performed within 28 days prior to registration, and participants must have an undetectable HBV viral load on suppressive therapy within 28 days prior to registration. Participants found to be HBV carriers during screening are eligible and must receive standard of care prophylaxis. Participants with active hepatitis B (HBV viral load \> 500 IU/mL) within 28 days prior to registration are not eligible
* Participants with a known history of hepatitis C virus (HCV) infection must have an undetectable HCV viral load within in 28 days prior to registration
* Participants must not have known lymphomatous involvement of the central nervous system (CNS)
* Participants must not have active inflammatory bowel disease (such as, Crohn's disease, ulcerative colitis), celiac disease (i.e., sprue), prior gastrectomy or upper bowel removal, or any other gastrointestinal disorder or defect that would interfere with the absorption, distribution, metabolism, or excretion of the study drug and/or predispose the subject to an increased risk of gastrointestinal toxicity
* Participants must not have a history of acute leukemia having been treated with intensive induction therapy. 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
* Participants must not have received any prior cytotoxic chemotherapy or rituximab for treatment of the newly diagnosed DLBCL except for the pre-phase treatment (within specified dose range) that may have either started before or may start after registration to S1918. Inhaled, nasal, and topical steroid use is allowed. Prior cytotoxic chemotherapy and/or antibody therapy for an indolent lymphoma prior to transformation is allowed. Up to 4 doses of intrathecal (IT) chemotherapy administered for central nervous system (CNS) prophylaxis is allowed in addition to protocol therapy. High-dose intravenous methotrexate is not allowed.
* Participants must not have received more than a cumulative of dose 250 mg/m\^2 of prior doxorubicin (or equivalent dose of another anthracycline, such as epirubicin) therapy (at any time prior to registration).
* Participants must not currently be receiving any other investigational agents
* Participant must not have a history of allergic reactions attributed to azacitidine, mannitol, or other hypomethylating agents
* Participants must be age ≥ 75
* Participants must have a Zubrod performance status of 0-2
* Participants must have adequate renal function, as demonstrated by a creatinine clearance, calculated by the Cockcroft and Gault formula, of \>= 30 ml/min that was obtained within 28 days prior to registration
* Aspartate aminotransferase (AST) =\< 2.5 x institutional upper limit of normal (IULN), alanine aminotransferase (ALT) =\< 2.5 x IULN (within 28 days prior to registration)
* Total bilirubin =\< 2 x institutional upper limit of normal (IULN), unless due to Gilbert's disease, hemolysis, or lymphomatous involvement of liver (within 28 days prior to registration). Note: If total bilirubin is elevated, and direct bilirubin is subsequently performed (within 28 days prior to registration) and resulted to be =\< 2 x IULN, the participant will be considered eligible
* Absolute neutrophil count (ANC) \>= 1000/mcL (within 28 days prior to registration)
* Platelets \>= 75,000/mcL (within 28 days prior to registration)
* Hemoglobin (Hgb) \>= 8 g/ dL (within 28 days prior to registration)
* If there is a documented lymphomatous involvement of the bone marrow, bone marrow function within 28 days prior to registration, as evidenced by:

* ANC \>= 500/mcL
* Platelets \>= 50,000/mcL
* Hemoglobin (Hgb) \>= 8 g/ dL
* Participants must have a left ventricular ejection (LVEF) fraction \>= 45% as measured by echocardiogram or radionuclide (multigated acquisition scan \[MUGA\]) ventriculography within 56 days prior to registration
* For the duration of the study treatment period and for at least 4 months following the last dose of study drug, male participants must agree to use effective contraceptive methods during sexual contact with a female of childbearing potential (FCBP) and must agree to refrain from semen or sperm donation during the same timeframe. Effective contraceptive methods include a history of vasectomy, use of hormonal contraception or an intrauterine device (IUD) by the female partner, or use of condoms

* A FCBP is a sexually mature woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months)
* Participants must not have active infection (systemic fungal, bacterial, or viral infection) that is not controlled (defined as ongoing signs/symptoms related the infection without improvement despite appropriate antibiotics, antiviral therapy, and/or other treatment)
* Participants must not have active cardiac disease within 26 weeks prior to registration, including: symptomatic congestive heart failure (New York Heart Association \[NYHA\] class 4), unstable angina pectoris, hemodynamically unstable cardiac arrhythmia, or myocardial infarction
* Participants must not have \>= grade 2 neuropathy, by Common Terminology Criteria for Adverse Events (CTCAE) version (v.) 5.0, within 28 days prior to registration
* Participants must not have any other known uncontrolled intercurrent illness including, but not limited to ongoing psychiatric illness/social situations that would limit compliance with study requirements
* Participants must not have a concurrent primary malignancy undergoing active therapy. Exceptions: participants may have non-melanomatous skin cancers requiring only surgical intervention. Participants may have a history of early stage breast cancer or prostate cancer in remission after surgical and/or radiation therapy on adjuvant hormonal therapy only