OUTLINE: The following acronyms are used: ARA-C Cytarabine, NSC-63878 ASP Asparaginase, NSC-109229 CF Leucovorin, NSC-3590 CTX Cyclophosphamide, NSC-26271 DM Dexamethasone, NSC-34521 DNR Daunorubicin, NSC-82151 G-CSF Granulocyte Colony-Stimulating Factor, NSC-614629 LBL Lymphoblastic Lymphoma LCALKi1B Large Cell Anaplastic B-cell Lymphoma LCALKi1T Large Cell Anaplastic T-cell Lymphoma LCL Large Cell Lymphoma Mesna Mercaptoethane Sulfonate, NSC-113891 MTX Methotrexate, NSC-740 TMP-SMX Trimethoprim-Sulfamethoxazole VCR Vincristine, NSC-67574 VP-16 Etoposide, NSC-141540 Induction: 2-Drug Combination Systemic Chemotherapy plus Single-Agent Intrathecal Chemotherapy followed by 2- or 3-Drug Combination Systemic Chemotherapy plus Single-Agent Intrathecal Chemotherapy. Part I: CTX/DNR; plus IT ARA-C; followed by Part II: DM/VCR; plus ASP for patients with LBL, T-cell LCL, or LCALKi1T; plus IT MTX. Consolidation: 2- or 3-Drug Combination Systemic Chemotherapy with Leucovorin Rescue followed by 2- or 3-Drug Combination Systemic Chemotherapy. Part I: ARA-C/MTX with CF; plus ASP for patients with LBL, T-cell LCL, or LCALKi1T; followed by Part II: ARA-C/VP-16; plus, for patients with LBL, T-cell LCL, or LCALKi1T. Maintenance. Single-Agent Systemic Chemotherapy with Leucovorin Rescue plus Single-Agent Intrathecal Chemotherapy followed sequentially by 3 2-Drug Combination Systemic Chemotherapy Regimens. Part I: MTX; with CF; plus IT MTX; followed by Part II: CTX/VCR; followed by Part III: ARA-C/VP-16; followed by Part IV: DNR/DM.