Patients with pre-B cell lymphoma then proceed to maintenance therapy. Patients with T cell lymphoma proceed to reinduction therapy. Reinduction A is a 4 week course of chemotherapy administered during months 1, 3, and 5 and consists of vincristine IV on day 1; methotrexate IV over 3 hours on days 1, 8, 15, and 22; methotrexate and methylprednisolone IT on day 2; asparaginase IM or IV on day 2; and oral mercaptopurine. Reinduction B is also a 4 week course of therapy administered during months 2, 4, and 6. This consists of oral prednisone twice a day on days 1-5; cytarabine subcutaneously twice a day on days 1-4; methotrexate IV on days 1, 8, 15, and 22; and oral mercaptopurine.