DISEASE CHARACTERISTICS: Histologically proven non-Hodgkin's lymphoma that has relapsed or failed to achieve complete remission after first line induction chemotherapy Intermediate or high grade (including mantle cell, but excluding lymphoblastic disease) No more than 1 prior salvage chemotherapy regimen, e.g.: Dexamethasone, high dose cytarabine, and cisplatin (DHAP) Etoposide, methylprednisolone, high dose cytarabine, and cisplatin (ESHAP) Low grade No more than 2 prior salvage chemotherapy regimens, e.g.: Fludarabine, mitoxantrone, and dexamethasone (FND) ESHAP DHAP OR Histologically proven stage III or IV Hodgkin's disease that has relapsed or failed to achieve remission after combination induction chemotherapy Prior primary radiotherapy allowed if relapse is high risk (e.g., recurrence in radiation field, B symptoms, liver/marrow involvement) No more than 2 prior salvage chemotherapy regimens Allogeneic stem cell transplantation group: Availability of 6 antigen (A, B, and DR loci) HLA matched sibling donor No active CNS disease A new classification scheme for adult non-Hodgkin's lymphoma has been adopted by PDQ. The terminology of "indolent" or "aggressive" lymphoma will replace the former terminology of "low", "intermediate", or "high" grade lymphoma. However, this protocol uses the former terminology.