Ibrutinib, Rituximab, Etoposide, Prednisone, Vincristine Sulfate, Cyclophosphamide, and Doxorubicin Hydrochloride in Treating Patients With HIV-Positive Stage II-IV Diffuse Large B-Cell Lymphomas

Inclusion Criteria: * Participants must have histologically (via at least a core or ideally, incisional or excisional biopsy) documented CD20 positive or negative diffuse large B-cell lymphoma (DLBCL) * Tissue available from the diagnostic biopsy in the form of blocks, tissue cores, or slides available for submission to central pathology is required for all participants enrolled to this study, for analysis of integral biomarkers. Formalin-fixed paraffin-embedded tissue from diagnostic tissue is acceptable and recommended; submission of the institutional diagnostic slides is also preferred for all participants enrolled in the study. Tissue and diagnostic slides are required to be submitted within 1 month of enrollment * Stage II-IV disease; participant will need measurable disease by computed tomography (CT) or positron emission tomography (PET) scans if enrolled in the dose-expansion cohort * HIV positive; documentation of HIV-1 infection by means of any one of the following: * Documentation of HIV diagnosis in the medical record by a licensed health care provider; * Documentation of receipt of ART (at least three different medications) by a licensed health care provider (documentation may be a record of an antiretroviral therapy (ART) prescription in the participant's medical record, a written prescription in the name of the participant for ART, or pill bottles for ART with a label showing the participant's name); * HIV-1 ribonucleic acid (RNA) detection by a licensed HIV-1 RNA assay demonstrating \> 1000 RNA copies/mL; * Any licensed HIV screening antibody and/or HIV antibody/antigen combination assay confirmed by a second licensed HIV assay such as a HIV-1 western blot confirmation or HIV rapid multispot antibody differentiation assay * NOTE: a "licensed" assay refers to a United States (U.S.) Food and Drug Administration (FDA)-approved assay, which is required for all investigational food drug (IND) studies * For the dose-finding cohort participants lymphoma must be untreated. For the dose-expansion cohort participants may have either untreated lymphoma or may have received prior therapy * Ages 18 - 64 * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 50%) * For the dose-finding cohort participants must have a CD4 count ≥ 100 cells/mm\^3. For the dose-expansion cohort participants may have any CD4 count, including a CD4 count \< 100 cells/mm\^3 * Absolute neutrophil count: \>= 1,000/mm\^3, unless decreased due to bone marrow involvement with lymphoma * Platelets: \>= 75,000/mm\^3, unless decreased due to bone marrow involvement with lymphoma * Total bilirubin: =\< 1.5 times the institutional upper limit of normal (ULN); if potentially due to lymphoma, in the dose-expansion cohort, the first cycle may be given without ibrutinib and if transaminitis and bilirubinemia improves to meet parameters, participant may be enrolled * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]): \< 2 times the institutional ULN; if potentially due to lymphoma, in the dose-expansion cohort, the first cycle will be given without ibrutinib and if transaminitis and bilirubinemia improves to meet parameters, participant may be enrolled * Creatinine levels below the normal institutional upper limits; or, creatinine clearance \>= 50 mL/min/1.73 m\^2 for participants with creatinine levels above institutional normal; unless decreased due to renal involvement by lymphoma * Participants must not be on medications, including antiretroviral (ARV) regimens such as cobicistat, indinavir, or ritonavir, or agents with moderate or strong CYP3A4 inhibition; if on a moderate or strong CYP3A4 inhibitor regimen prior to study enrollment, participants must be switched to a qualifying regimen with the last dose of the strong CYP3A4 inhibitor taken at least one week before administration of ibrutinib * Willingness of sexually active participants to use adequate contraception; both men and women of child-bearing potential treated or enrolled on this study must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) before study entry, for the duration of study participation, 90 days after completion of ibrutinib, and 12 months after the last dose of rituximab, whichever comes last; men who only have sex with other men do not need to use contraception specifically for this study (should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately) * All participants will be required to be screened for hepatitis B; all participants who present with acute hepatitis B or show normal transaminases and are hepatitis B surface antigen (HBsAg) positive (+) and IgM+ for hepatitis core antigen will not be eligible for trial enrollment; per Infectious Diseases Society of America (IDSA) and Assistance for AIDS Specific Drugs (AASD) guidelines, those participants that show no immunity, defined by the lack of hepatitis B surface antibody, and show evidence of chronic infection (i.e. hepatitis B \[HB\]sAg+, HBcore+, hepatitis B surface antibody \[HBsAB\] negative \[-\]) will be required to be on anti-hepatitis B therapy, during the study, in order to be eligible; the exact hepatitis B therapy will be at the discretion of the infection disease specialist or investigator; if infected with hepatitis B, participants will be permitted to enroll in the study provided liver function tests meet criteria listed above, there is no evidence of cirrhosis AND participants will be required to be on anti-hepatitis B therapy * All participants will be required to be screened for hepatitis C; if hepatitis C antibody positive, with or without a positive hepatitis C RNA level, participants will be permitted to enroll in the study provided liver function tests meet criteria listed, and have no evidence of cirrhosis; participants diagnosed with hepatitis C less than 6 months from trial enrollment will be considered to have acute hepatitis C, and will be excluded from study UNLESS hepatitis C viral load is undetectable * Adequate cardiac function defined as an ejection fraction on echocardiogram (ECHO) or multi-gated acquisition (MUGA) that is at or above the institutional normal limits. For the dose-expansion cohort, if the participant had a pre-treatment ECHO prior to pre-study therapy which reports adequate cardiac function defined as an ejection fraction on ECHO or MUGA that is at or above the institutional normal limits, a repeat ECHO will not need to be repeated prior to start of study treatment * Participants must be able to swallow oral pills * Ability to understand and willing to sign a written informed consent document Exclusion Criteria: * Participants who have had chemotherapy other than R-EPOCH, R-CHOP, or limited therapy, or radiotherapy other than palliative radiation for medical emergencies (like cord compression), within the last 4 weeks * For the dose-finding cohort prior cytotoxic chemotherapy or radiotherapy for this lymphoma is exclusionary. For the dose-expansion cohort participants may have received: * A maximum of one cycle of combination chemotherapy, including rituximab-containing regimens R-CHOP and R-EPOCH. The start of previous chemotherapy cycle must occur at least 21 days but no more than 28 days prior to beginning treatment under this protocol, and such cycle will count towards the maximum of 6 cycles under this study (i.e., cycle off study will count as cycle 1) OR * 1 prior cycle of limited therapy including cyclophosphamide and/or rituximab and/or glucocorticoids to improve hepatic or renal function impaired due to lymphoma involvement. The start of this therapy may occur up to 28 days prior to beginning treatment under this protocol; cyclophosphamide administration must have been completed at least 14 days prior to initiation of protocol therapy. Such treatment will not count towards the maximum of 6 cycles under this study (i.e., participants will receive 6 cycles on study) * For the dose-finding cohort rituximab within 12 months prior to study registration will be exclusionary; only exception will be if rituximab was given for indications other than the treatment of aggressive lymphoma. For the dose-expansion cohort one cycle of rituximab as part of R-CHOP or R-EPOCH or limited therapy may be administered off study prior to enrollment; prior rituximab will also be allowed if rituximab was given for indications other than the treatment of aggressive lymphoma * Participants who are receiving any other investigational agents * Participants who have previously received ibrutinib for another indication * Expected survival \< 2 months * Participants with a history of an opportunistic fungal infection or active fungal infection requiring, or at high risk of requiring, prophylactic or treatment with fluconazole, voriconazole or posaconazole * Participants with known brain metastases from solid tumors should be excluded from this clinical trial * Presence of second active tumor, other than non-melanoma skin cancer, carcinoma in situ of the cervix, or Kaposi's sarcoma (KS) that requires systemic therapy * For the dose-finding cohort, participants with known or suspected parenchymal brain, spinal cord, leptomeningeal disease prior to study enrollment will be excluded. For the dose-expansion cohort participants with known or suspected parenchymal brain or spinal cord disease, or symptomatic leptomeningeal disease will be excluded. Asymptomatic leptomeningeal disease will be allowed * History of allergic reactions attributed to compounds of similar chemical or biologic composition to ibrutinib or other agents used in study * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that, in the opinions of the investigator, would limit compliance with study requirements * Pregnancy or breastfeeding; a pregnancy test must be performed within 7 days prior to ibrutinib initiation in women of childbearing potential; pregnant women; breastfeeding must be discontinued because of unknown but potential risks in the nursing infant * Unable to comply with the requirements of the protocol, or unable to provide adequate informed consent in the opinion of the principal investigator * Serious, ongoing, non-malignant disease or infection, which in the opinion of the investigator and/or the sponsor would compromise other protocol objectives; participants with active opportunistic infections are ineligible * Major surgery, other than diagnostic surgery, occurring 4 weeks prior to study entry; splenectomy will not be considered an exclusionary major surgery * History of cutaneous or mucocutaneous reactions, or diseases in the past, due to any cause, severe enough to cause hospitalization or an inability to eat or drink for \> 2 days; this exclusion relates to the long-term possibility of severe cutaneous or mucocutaneous reactions to rituximab that might occur at increased frequency in participants who have had severe skin disease or reactions in the past * Myocardial infarction (MI) within 6 months prior to study entry, New York Heart Association (NYHA) class II or greater heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, clinically significant pericardial disease, or electrocardiographic evidence of acute ischemic or active conduction system abnormalities