OUTLINE: Patients are stratified according to participating institution and descriptive factors: histopathology (diffuse large cleaved/noncleaved and immunoblastic lymphomas vs all others), CD4 count (less than 50 vs 50 or more cells/mm3), prior opportunistic infection (yes vs no), performance status (0 and 1 vs 2), concurrent AZT (yes vs no), concurrent protease inhibitors (yes vs no), marrow involvement (yes vs no). Patients receive ProMACE-CytaBOM regimen as follows: Cyclophosphamide, doxorubicin, and etoposide IV on day 1 Cytarabine, bleomycin, vincristine, and methotrexate IV on day 8 Oral prednisone on days 1-14 Oral leucovorin calcium every 6 hours for 4 doses on day 9 Patients also receive filgrastim (G-CSF) subcutaneously on days 9-20 and oral co-trimoxazole 3 days a week throughout treatment, plus antiretroviral therapy at the discretion of the treating physician. Treatment repeats every 21 days for a maximum of 6 courses. Patients with progressive disease are removed from study after 2 courses. Remaining patients receive an additional 2 treatment courses and are then restaged. Patients without stable or progressive disease receive 2 more courses in the absence of unacceptable toxicity. Patients with positive bone marrow at study entry receive CNS prophylaxis with 5 evenly spaced doses of intrathecal cytarabine during the first 2 treatment courses and on day 1 of each subsequent course. Patients with positive CSF cytology at study entry receive intrathecal cytarabine on days 1-5 of the first treatment course and on day 1 of each subsequent course if CSF negative after 5 daily doses. Patients whose CSF remains positive after 5 days receive 5 evenly spaced doses of intrathecal methotrexate during the second treatment course. Patients with negative bone marrow and CSF cytology at study entry receive 5 evenly spaced doses of intrathecal cytarabine within 1 month of systemic therapy. All patients achieving a complete or partial response following systemic therapy and intrathecal cytarabine receive cranial irradiation to all meningeal surfaces. Patients are followed monthly for 1 year, every 2 months for 1 year, every 3 months for 1 year, then annually thereafter.