Brief Summary: This phase I/II trial studies the side effects and best dose of lenalidomide when given together with combination chemotherapy and to see how well they work in treating patients with v-myc myelocytomatosis viral oncogene homolog (avian) (MYC)-associated B-cell lymphomas. Lenalidomide may stop the growth of B-cell lymphomas by blocking the growth of new blood vessels necessary for cancer growth and by blocking some of the enzymes needed for cell growth. Biological therapies, such as lenalidomide, use substances made from living organisms that may stimulate or suppress the immune system in different ways and stop cancer cells from growing. Drugs used in chemotherapy, such as etoposide, prednisone, vincristine sulfate, doxorubicin hydrochloride, cyclophosphamide, 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 antibodies, such as rituximab, may block cancer growth in different ways by targeting certain cells. Giving lenalidomide together with combination chemotherapy may be an effective treatment in patients with B-cell lymphoma.

Detailed Description: PRIMARY OBJECTIVES: I. To determine the maximum tolerated dose (MTD) of lenalidomide when added to dose-adjusted (DA)-etoposide, prednisone, vincristine sulfate, doxorubicin hydrochloride, cyclophosphamide, rituximab (EPOCH-R) (hereby termed "DA-EPOCH-RR") in patients with double hit lymphoma (DHL) lymphomas. (Phase I) II. To determine the 1- and 2-year progression free survival (PFS) of DA-EPOCH-RR in patients with DHL lymphomas. (Phase II) SECONDARY OBJECTIVES: I. Overall response rate, complete response, and duration of response. II. Quality of life (QOL) measures using standardized scales. III. Toxicity assessment using version 4.0 of the National Cancer Institute (NCI)-Common Terminology Criteria for Adverse Events (CTCAE) criteria. IV. Overall survival (OS) at 1 and 2 years. OUTLINE: This is a phase I, dose-escalation study of lenalidomide followed by a phase II study. INDUCTION PHASE: Patients receive lenalidomide orally (PO) daily on days 1-14. Treatment repeats every 21 days for 6 courses in the absence of disease progression or unacceptable toxicity. DA-EPOCH-R: Patients receive etoposide intravenously (IV) continuously on days 1-4, prednisone PO twice daily (BID) on days 1-5, vincristine sulfate IV continuously on days 1-4, doxorubicin hydrochloride IV continuously on days 1-4, cyclophosphamide IV over 15 minutes on day 5, and rituximab IV over 4 hours on day 1 (per institutional guidelines). Treatment repeats every 21 days for 6 courses in the absence of disease progression or unacceptable toxicity. CONSOLIDATION PHASE: Patients who are transplantation (hematopoietic stem cell transplant \[HSCT\])-eligible receive BCNU, etoposide, cytarabine, and melphalan (BEAM)-conditioning regimen followed by autologous (auto)-HSCT or HSCT at the discretion of the treating physician. Patients who do not undergo HSCT in first remission receive lenalidomide maintenance for 12 months. After completion of study treatment, patients are followed up for every 3 months for 1 year, every 4 months for 1 year, and then periodically for 1 year.