Patients who received organ or allogeneic bone marrow or peripheral blood stem cell transplants Previous use of investigational agents, chemotherapy or immunotherapy for lymphoma any time prior to enrollment (i.e. must have untreated disease); prior allogeneic or autologous transplants are also not allowed Prior allogeneic hematopoietic stem cell transplants Two prior stem cell transplants of any kind. Patients who had solid organ transplants are not eligible More than one prior transplant prior to study entry with the exception of tandem transplantation; tandem transplantation is defined as two autologous stem cell transplants that occur within 9 months of one another, and the patient did not have disease progression in the period between the two transplants History of a major organ allograft or condition requiring chronic immunosuppression, e.g., kidney, liver, lung, heart, bone marrow transplant, or autoimmune diseases; this includes treatment with corticosteroids within one month (dose of >= 10 mg/day methylprednisolone equivalent) (excluding inhaled steroids); patients who have received corneal transplants, cadaver skin, or bone transplants are eligible Two prior stem cell transplants of any kind Patients with prior stem cell transplants. Patients who have received organ transplants. Undergone an organ transplant(s) including allogeneic stem cell or bone marrow transplants must have received at least 1 but no greater than 2 prior lines of therapy (note: induction and stem cell transplants with or without maintenance therapy is considered 1 line of therapy) Patients are eligible >= 6 weeks after autologous stem cell transplants or stem cell infusions as long as hematologic and other eligibility criteria have been met Patients who have received allogenic stem cell transplants Two prior stem cell transplants of any kind Patients with prior autologous stem cell transplants will be included; patients with prior allogeneic stem cell transplants will be eligible for 2nd BMT if not previously transplanted with FLT on 11-c-0136 Non-Hodgkin's lymphoma with chemoresponsive disease in any of the following categories: \r\n* High grade lymphomas who have failed to achieve a first CR or have relapsed following a 1st remission who are not candidates for autologous transplants or transplants requiring the use of calcineurin inhibitors\r\n* Any NHL with therapy responsive disease which is considered not curable outside the transplant setting and not eligible/appropriate for autologous transplant or a higher priority protocol Peripheral autologous stem cell transplant within 12 weeks prior to Baseline; prior allogeneic transplants within 16 weeks or chronic use of immunosuppressants. Have had previous transplants and/or prior mobilization attempts Subjects with organ transplants Patients with prior allogenic transplants. Allogeneic transplant recipients undergoing fully ablative transplants CD34 selection or total cell depletion outside haploidentical transplants Must be candidates for peripheral blood stem cell transplants. Participant is candidate for hematopoietic stem cell transplants at the time of enrollment.