 This phase I trial studies the side effects and best dose of fludarabine fludarabine phosphate when given together with iodine I 131 tositumomab in treating older patients who are undergoing an autologous or syngeneic stem cell transplant for relapsed or refractory B-cell non-Hodgkins lymphoma NHL. Radiolabeled monoclonal antibodies, such as iodine I 131 tositumomab, can find cancer cells and carry cancer-killing substances to them without harming normal cells. Drugs used in chemotherapy, such as fludarabine, work in different ways to stop the growth of cancer cells, either by killing the cells or by stopping them from dividing. A peripheral stem cell transplant may be able to replace blood-forming cells that were destroyed by chemotherapy and radiation therapy. Giving iodine I 131 tositumomab together with fludarabine followed by autologous stem cell transplant may be an effective treatment for NHL 