Patients receive everolimus orally (PO) once daily (QD) on days 1-10 or 1-14; rituximab IV, cyclophosphamide IV, doxorubicin hydrochloride IV over 15-60 minutes, and vincristine sulfate IV on day 1; and prednisone PO QD on days 1-5. Treatment repeats every 21 days for up to 6 courses in the absence of disease progression or unacceptable toxicity.