I. To evaluate engraftment of human leukocyte antibody (HLA) identical peripheral blood stem cell (PBSC) allografts given after conditioning with total-body irradiation (TBI) (200cGy) +/- fludarabine (fludarabine phosphate), 90 mg/m^2 and post-grafting immunosuppression with cyclosporine (CSP)/mycophenolate mofetil (MMF) in refractory or relapsed lymphoma patients following an initial autologous peripheral blood stem cell transplant (PBSCT) for disease cytoreduction.