DISEASE CHARACTERISTICS: Histologically confirmed intermediate or high grade non-Hodgkin's lymphoma, acute myelogenous leukemia, or acute lymphocytic leukemia that is refractory to or relapsed after prior therapy Must be HIV seropositive confirmed by Western blot Must have a 6/6 HLA matched sibling donor or 6/6, 5/6, or 4/6 HLA matched umbilical cord blood (UCB) from the New York Blood Center's Unrelated UCB Bank that is not homozygous for the CCR-5 mutation No active primary CNS lymphoma or chronic CNS infection No history of AIDS defining opportunistic infection or active invasive aspergillus infection 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.