Patients undergo blood and cerebrospinal fluid collection and tumor biopsies periodically during study treatment for correlative studies of prognostic biomarkers predictive of survival (e.g., c-flip protein expression; p53 mutations [by immunohistochemistry (IHC)]; multidrug resistance gene expression [by IHC]; and Epstein-Barr virus in tumor DNA or cerebrospinal fluid [by polymerase chain reaction]); genotyping of Burkitt's lymphoma; and flow cytometry as a tool (by staining) for detecting occult positivity of leptomeningeal disease in Burkitt's lymphoma.