 This pilot clinical trial studies gene therapy following combination chemotherapy in treating patients with acquired immune deficiency syndrome AIDS-related non-Hodgkin lymphoma. Placing genes that have been shown in the laboratory to inhibit the growth and spread of the immunodeficiency virus HIV into the patients peripheral blood stem cells may improve the bodys ability to fight HIV. Drugs used in chemotherapy work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving gene therapy after combination chemotherapy may improve the bodys ability to fight HIV and AIDS-related non-Hodgkin lymphoma. 