OBJECTIVES: I. Assess the feasibility of treating all histologic subgroups of pediatric non-Hodgkin's lymphoma on one protocol, with the addition of asparaginase during the induction and consolidation phases for diffuse lymphoblastic lymphoma and T-cell, large noncleaved cell diffuse lymphoma. II. Assess whether intensification of cyclophosphamide during induction therapy will achieve a complete response rate of 95% in 1 to 1.5 months for all histologies. III. Assess whether achieving remission induction in 1 month, administering cytarabine/methotrexate by continuous infusion during consolidation therapy, and increasing the number of intrathecal methotrexate injections throughout protocol therapy decreases central nervous system relapse in these patients. IV. Assess whether a 5-year recurrence-free survival of 85% is achievable for all histologies on this protocol. V. Assess whether duration of maintenance chemotherapy may be stratified by stage and histology of disease to avoid unnecessarily prolonged chemotherapy.