Gemcitabine Hydrochloride, Clofarabine, and Busulfan Before Donor Stem Cell Transplant in Treating Patients With Refractory B-Cell or T-Cell Non-Hodgkin Lymphoma or Hodgkin Lymphoma

This phase I/II trial studies the side effects and best dose of gemcitabine hydrochloride, clofarabine, and busulfan before donor stem cell transplant and to see how well it works in treating patients with B-cell or T-cell non-Hodgkin lymphoma or Hodgkin lymphoma that does not respond to treatment. Giving chemotherapy before a donor bone marrow or peripheral blood stem cell transplant helps stop the growth of cancer cells. It may also stop the patient's immune system from rejecting the donor's stem cells. When the healthy stem cells from a donor are infused into the patient they may help the patient's bone marrow make stem cells, red blood cells, white blood cells, and platelets.