To determine the safety and toxicity of high-dose systemic methotrexate (MTX) and dexamethasone (DEX) combined with zidovudine (AZT) and brain irradiation in patients with AIDS-related primary central nervous system (CNS) lymphoma and to determine response rates and survival of treated patients. Also to determine if the treatment inhibits HIV replication in patients who are HIV culture and/or antigen positive and to assess the incidence of opportunistic infection in these patients Results of radiation given to patients with AIDS-related high-grade CNS lymphoma have been disappointing, with short survival times due to infection complications. However, complete response has been documented after radiation in some patients. High-dose MTX will be used to improve the possibility of a greater antineoplastic response than that obtained by radiation alone. Since the underlying immunodeficiency state is not affected by therapy directed against the lymphoma, patients are still prone to life-threatening opportunistic infections or relapse of lymphomatous disease within the CNS. Accordingly, AZT will also be used in an attempt to alter the overall natural history of the disease.