OUTLINE: Patients are stratified according to disease characteristics. All patients receive a 30 minute infusion of doxorubicin HCl liposome IV, cyclophosphamide IV, and vincristine IV on day 1. Patients also receive oral prednisone on days 1-5. Filgrastim (G-CSF) is administered subcutaneously starting on day 6 and continues until the absolute neutrophil count is at least 10,000/mm3. Treatment courses are repeated every 21 days. Patients with lymphomatous bone marrow involvement and/or category J lymphoma receive cytarabine and methotrexate intrathecally weekly for 4 weeks. Patients with lymphomatous meningitis receive whole brain irradiation and an alternating intrathecal chemotherapy regimen. A minimum of 4 and a maximum of 8 courses are administered. Patients are removed from the study for progressive disease, stable disease after 4 courses, a life threatening infection that would delay treatment for more than 6 weeks, or any delay, except due to neutropenia, in chemotherapy treatment for more than 6 weeks. Patients who achieve a complete response receive an additional 2 courses of therapy. Patients are followed every 3 months for 2 years, every 6 months for 3 years, and annually thereafter.