Combination Chemotherapy and Rituximab in Treating Patients With Newly Diagnosed AIDS-Related B-Cell Non-Hodgkin's Lymphoma

DISEASE CHARACTERISTICS: * Histologically or cytologically confirmed AIDS-related B-cell non-Hodgkin's lymphoma (NHL), including any of the following subtypes: * Grade III follicular large cell lymphoma * Diffuse large B-cell lymphoma * Immunoblastic lymphoma * Plasmablastic lymphoma * Primary effusion lymphoma * Previously untreated disease * Any stage disease * CD20 positive disease * Must have documented HIV infection * Documentation may be by serology (enzyme-linked immunosorbent assay, western blot), culture, or quantitative polymerase chain reaction or branched DNA assays * Prior documentation of HIV seropositivity allowed * Measurable or nonmeasurable disease * Currently receiving effective highly active anti-retroviral therapy * No primary CNS lymphoma, including parenchymal brain or spinal cord lymphoma * No presence of leptomeningeal disease (positive cerebrospinal fluid for lymphoma) or presence of metastatic disease to brain, in terms of any mass lesion PATIENT CHARACTERISTICS: * ECOG performance status (PS) 0-2 OR Karnofsky PS 50-100% * Life expectancy ≥ 2 months * Absolute granulocyte (neutrophil) count ≥ 1,000/mm³ (unless secondary to lymphomatous involvement of bone marrow) * Platelet count ≥ 75,000/mm³ (unless secondary to lymphomatous involvement of bone marrow or due to HIV-related thrombocytopenia) * Bilirubin ≤ 2.0 mg/dL (unless elevated secondary to lymphomatous involvement of liver or biliary system or due to other HIV medications \[e.g., indinavir, tenofavir, or atazanavir\]) * SGOT ≤ 5 times upper limit of normal * Creatinine ≤ 2.0 mg/dL OR creatinine clearance ≥ 60 mL/min (unless secondary to renal involvement by lymphoma) * LVEF normal by MUGA or echocardiogram * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for 6 months after completion of study treatment * No other malignancy, except nonmelanoma skin cancer, carcinoma in situ of the cervix, or Kaposi's sarcoma that does not require systemic therapy * No serious, ongoing, nonmalignant disease or infection that would preclude study compliance, in the opinion of the investigator * No 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 * No acute, intercurrent infection that would preclude study treatment * Patients with Mycobacterium avium are eligible * No cardiovascular problems, including any of the following: * Myocardial infarction within the past 6 months * New York Heart Association class II-IV heart failure * Uncontrolled angina * Severe uncontrolled ventricular arrhythmias * Clinically significant pericardial disease * ECG evidence of acute ischemic or active conduction system abnormalities. * No shortness of breath at rest * Arterial PO\_2 ≥ 70 or pulse oximeter-derived O\_2 saturation ≥ 94% on room air (unless due to lymphomatous involvement of the lungs) * Able to comply with study and provide adequate informed consent PRIOR CONCURRENT THERAPY: * See Disease Characteristics * At least 4 weeks since prior major surgery (except diagnostic surgery) * At least 12 months since prior rituximab unless it was only given for indications other than the treatment of aggressive lymphoma * No prior cytotoxic chemotherapy or radiotherapy for this lymphoma * Concurrent radiotherapy, with or without steroids, for emergency conditions secondary to lymphoma (i.e., CNS tumor or cord compression) allowed * No zidovudine or zidovudine-containing regimen (including Combivir® or Trizivir®) during and for 2 months after completion of chemotherapy * Concurrent erythropoietin or filgrastim (G-CSF) allowed * Growth factor therapy must be discontinued ≥ 24 hours prior to study entry