<qa>  What is the best chance for cure of leukemia or lymphoma?This is a research study involving the treatment of leukemia or lymphoma lymph gland cancer in adults who have leukemia or lymphoma that is unlikely to be cured with regular anticancer drugs or radiation treatments. Intensive treatment with high doses of chemotherapy followed by a bone marrow transplant BMT from an HLA-tissue-type matched related donor would provide the best chance for cure of this leukemia or lymphoma. However, the success of BMT from relatives is limited in patients who are older than 50 years andor have organ dysfunction by substantial complications due to the high dose chemotherapy related toxicity, graft-versus- host disease GVHD, and relapse. Patients eligible for this study have an HLA matched sibling, but a BMT from the sibling would carry a high risk for severe side effects due to the patients age, andor organ dysfunction. 