All patients will receive combination chemotherapy and AZT. The combination chemotherapy will be repeated every 3 to 4 weeks for a maximum total of 6 cycles. Each cycle will consist of doxorubicin, bleomycin, cyclophosphamide, and vincristine on day 1, dexamethasone on days 1-5, and methotrexate on day 15. Patients with meningeal or bone marrow disease will receive radiation and intrathecal cytarabine (ARA-C) while those without will receive ARA-C without radiation. Patients with documented lymphomas in the central nervous system at initial workup will start radiation as soon as possible and intrathecal ARA-C (t.i.w. until cerebrospinal fluid is clear then every month for 1 year); patients with normal lumbar puncture, brain scan, and bone marrow at first diagnosis will begin radiation on day 1 of cycle 3 of chemotherapy. Lumbar punctures for evaluation will be done four times during the first cycle, on days 1, 8, 21, and 28. AZT will be administered every 4 hours, 7 days a week, beginning at the completion of combined chemotherapy, once the patient has achieved a complete remission of the lymphoma, and continuing for 1 year.