Study of Pomalidomide Combined With Modified DA-EPOCH and Rituximab in KSHV-Associated Lymphomas

Background: \- The chemotherapy combination DA-EPOCH-RP includes the drugs etoposide (E), prednisone (P), vincristine (O), cyclophosphamide (C), doxorubicin (H), rituximab (R), and pomalidomide (P). Researchers want to see if including pomalidomide will help people with two rare lymphomas. Objectives: \- To study the safety and efficacy of the chemotherapy drugs DA-EPOCH-RP. Eligibility: \- Adults at least 18 years old. They must have primary effusion lymphoma or large cell lymphoma arising from Kaposi sarcoma Herpesvirus-associated multicentric Castleman disease. Design: * Participants will be with screened with blood tests, scans, spinal tap, and bone marrow sample. They may have skin or lymph node samples taken and fluid removed from around some organs. * Participants will have breathing and eye tests. A camera may take pictures inside their body. * Participants will take pomalidomide alone by mouth for up to 21 days. Then they will get rituximab by intravenous (IV) catheter, which is a small tube that goes into a vein.. * Participants will have an IV inserted in an arm or chest vein to get the IV chemotherapy drugs, at the same time the will take pomalidomide by mouth for 5 days. * They will get DA-EPOCH-RP in 21-day cycles. Most people will have 6 cycles. * They will get 4 study drugs by IV for 5 days and 2 others by mouth for 5 days. * They will get daily filgrastim injections in the skin until white blood counts are acceptable * For 2 days of some cycles, methotrexate will be injected into the spinal fluid. * After completing EPOCH-RP, some participants who have Kaposi sarcoma will be prescribed pomalidomide for 3-weeks, followed by a one week break, for up to 12 months. * Participants will repeat the blood tests often. They will also have repeated medical history, physical exam, urine and stool tests, and pictures of any rashes associated with these lymphomas. * Participants will have several follow-up visits over 4 years.