Combination Chemotherapy and Rituximab in Treating Patients With HIV-Associated Stage I, Stage II, Stage III, or Stage IV Non-Hodgkin's Lymphoma

Inclusion Criteria:

* Previously untreated histologically or cytologically documented B-cell non-Hodgkin's lymphoma; the following histologies are eligible: diffuse large B-cell lymphoma, high-grade large cell immunoblastic lymphoma, anaplastic large cell lymphoma, Burkitt's lymphoma, high-grade B-cell lymphoma, Burkitt-like (small non-cleaved lymphoma)
* Tumors must be CD20 positive
* Documented HIV infection: documentation may be serologic (ELISA, western blot), culture, or quantitative PCR or bDNA assays
* Evaluable or measurable disease
* Stage I and IE or Stage II-IV disease patients
* ANC \>= 1000 cells/mm\^3
* Platelet count \>= 75,000/mm\^3 unless cytopenias are secondary to lymphoma
* All patients must be off colony stimulating factor therapy at least 24 hours prior to chemotherapy
* Transaminase =\< 5 times the upper limit of normal unless secondary to hepatic infiltration with lymphoma or isolated hyperbilirubinemia associated with the use of indinavir or other antiretrovirals
* Total Bilirubin \< 2.0 unless secondary to hepatic infiltration with lymphoma or isolated hyperbilirubinemia associated with the use of indinavir or other antiretrovirals; for bilirubin \> 3.0 due to hepatic involvement the initial dose of doxorubicin will be decreased by 50% and the initial dose of vincristine will be omitted
* Creatinine \< 2.0 unless due to lymphoma
* KPS \>= 50 (ECOG PS 0, 1, or 2)
* Able to give consent
* Female patients must have a negative pregnancy test within 72 hours of entering into the study; males and females must agree to use adequate birth control if conception is possible during the study; women must avoid pregnancy and men avoid fathering children while in the study
* Patients already receiving erythropoeitin or G-CSF are eligible
* Patients must have a left ventricular ejection fraction that is at or above the lower institutional limits of normal, as assessed by nuclear scan or echocardiogram obtained within 12 weeks of registration
* Lymphomatous meningitis (patients with a positive CSF cytology are eligible)

Exclusion Criteria:

* Previous chemotherapy or radiotherapy for this lymphoma
* Primary Central Nervous System Lymphoma (parenchymal brain or spinal cord tumor)
* Acute active HIV-associated opportunistic infection requiring antibiotic treatment; patients with mycobacterium avium are not excluded; chronic therapy with potentially myelosuppressive agents is allowed provided that entry hematologic criteria are met
* Concurrent malignancy (excluding in situ cervical cancer, or non-metastatic non-melanomatous skin cancer, or Kaposi's sarcoma not requiring systemic chemotherapy)
* Previous therapy with rituximab within 12 months; patients treated with rituximab more than 12 months earlier are eligible only if it was given for indications other than the treatment of intermediate- or high-grade lymphoma (eg, low-grade lymphoma or ITP)