This randomized phase II trial is studying how well giving combination chemotherapy together with rituximab works in treating patients with HIV-associated stage I, stage II, stage III, or stage IV non-Hodgkin's lymphoma. Drugs used in chemotherapy work in different ways to stop cancer cells from dividing so they stop growing or die. Monoclonal antibodies such as rituximab can locate cancer cells and either kill them or deliver cancer-killing substances to them without harming normal cells. Combining chemotherapy with monoclonal antibody therapy may kill more cancer cells.