Intravenous Chemotherapy or Oral Chemotherapy in Treating Patients With Previously Untreated Stage III-IV HIV-Associated Non-Hodgkin Lymphoma

Inclusion Criteria: * Ability to understand and the willingness to provide written informed consent to participate * Adults, 18 years of age or older; date of birth should be determined based on the best possible information or source documentation available * HIV-1 infection, documented by any licensed rapid HIV test or HIV enzyme or chemiluminescence immunoassay (E/CIA) test kit at any time prior to study entry and confirmed by a licensed Western blot or a second antibody test by a method other than the initial rapid HIV and/or E/CIA, or confirmed by HIV-1 antigen or plasma HIV-1 ribonucleic acid (RNA) viral load \> 1,000 copies/mL * NOTE: the term "licensed" refers to a United States (U.S.) Food and Drug Administration (FDA)-approved kit or for sites located in countries other than the United States, a kit that has been certified or licensed by an oversight body within that country and validated internally * WHO (World Health Organization) and CDC (Centers for Disease Control and Prevention) guidelines mandate that confirmation of the initial test result must use a test that is different from the one used for the initial assessment; a reactive initial rapid test should be confirmed by either another type of rapid assay or an E/CIA that is based on a different antigen preparation and/or different test principle (e.g., indirect versus competitive), or a Western blot or a plasma HIV-1 RNA viral load * Biopsy-proven, measurable or assessable systemic NHL that has been confirmed by an AIDS Malignancy Clinical Trial Consortium (AMC)-approved site pathologist; if a hard copy of the pathology report is unavailable at the time of enrollment, a verbal report by the pathologist confirming the diagnosis must be documented in the medical chart * Pathology slides from tumor tissue obtained by surgical excision or core biopsy must be reviewed by the designated site pathologist, or backup pathologist, prior to study entry; confirmation of the diagnosis must be documented by the AMC-approved pathologist prior to study entry; please reference the AMC-068 Manual of Procedures (MOP) for further instructions on documenting the diagnosis; the site pathologist for NHL must be approved through the AMC's external quality assessment (EQA) process * Participants must have fifteen blank(unstained) slides or a diagnostic tissue block must be available for central pathology review by the AMC Core Pathology Laboratory * Eastern Cooperative Oncology Group (ECOG) performance status of 0-3 * Participants must have an estimated life expectancy of \> 6 weeks * White blood cells (WBC) \>= 3,000 cells/uL (3.0 x 10\^9 L) or * Absolute granulocytes \>= 1500 cells/uL (1.5 x 10\^9 L) * Platelets \>= 100,000 cells/uL (75 x 10\^9 L) * Hemoglobin \> 8 g/dL (5.0 mmol/L) * Patients may enroll with lower hematologic values, if bone marrow involvement is documented; in this case, patients should be transfused to hemoglobin \> 8 g/dL * Serum creatinine \< 3.0 mg/dL (265.2 umol/L) * Total bilirubin =\< 1.5 institutional upper limit of normal (ULN), unless elevated secondary to lymphomatous involvement of liver or biliary system, or due to other HIV medications (e.g., indinavir, tenofovir, or atazanavir); if secondary to lymphomatous involvement, an initial upper limit of total bilirubin 5 mg/dL (85.5 uM/L) should be utilized - for direct bilirubin \> 1.2 mg/dL (20.5 uM/L) * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 2.5 institutional ULN (unless elevated secondary to lymphomatous involvement of the liver) * Participants must have a lumbar puncture with negative cerebral spinal fluid cytology within 6 weeks prior to enrollment; participants must be without evidence for central nervous system (CNS) lymphoma on neurological exam and have no radiographic evidence (if radiographic studies are done) of CNS lymphoma (inclusive of parenchymal, vitreal, or leptomeningeal involvement) * Participants must not have had any prior chemotherapy or radiation therapy and no more than 10 days of corticosteroids in the preceding 30 days prior to enrollment * All participants must be prescribed combination antiretroviral therapy with the goal of virological suppression using an acceptable regimen that adheres to national guidelines for treatment of HIV infection; non-suppressed, treatment experienced patients, defined as patients with a viral load \> 400 copies/mL who have been on antiretroviral therapy for more than 4 months can be enrolled if an alternative antiretroviral therapy (ART) regimen is available that includes at least two ART drugs that, in the opinion of the site investigator, are expected to have activity based on genotypic testing (if available) and treatment history; patients are not allowed to receive zidovudine (azidothymidine \[AZT\]) as part of concurrent chemotherapy and ART regimen, since it is myelosuppressive; zidovudine may be discontinued and substituted as clinically indicated prior to or at the time of enrollment. * Participants of childbearing potential, defined as 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), must have a pregnancy test within 7 days prior to enrollment and agree to use an effective form of contraception (e.g., barrier contraception, highly effective hormonal contraception) * Participants are allowed to have an active infection(s) for which they are receiving drug treatment provided the clinical status is judged to be stable and survival is estimated to be at least 6 weeks * Participants must, in the opinion of the investigatory, be capable of complying with the protocol * Participants must be able to take oral medications * Participants must have a CD4 count performed within 30 days of enrollment Exclusion Criteria: * Inability to provide informed consent * A medical or psychiatric illness that precludes ability to give informed consent or is likely to interfere with the ability to comply with the protocol stipulations * Participants with circumstances that will not permit completion of the study or required follow-up; for instance, if travel to and from treatment site is an issue * Pregnant or breastfeeding * Inability to swallow oral medications