This randomized phase II/III trial studies how well combination chemotherapy with or without
rituximab works in treating younger patients with stage III-IV non-Hodgkin lymphoma or
B-cell acute leukemia. 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. Monoclonal antibody, such as rituximab, may block cancer growth in
different ways by targeting certain cells. It is not yet known whether combination
chemotherapy together with rituximab is more effective in treating patients with non-Hodgkin
lymphoma or B-cell acute leukemia.