Additional Study Information: The purpose of this study is to test the safety and tolerability (side effects) of adding a study drug called lenalidomide at different doses in combination with the usual treatment with EPOCH chemotherapy. Dose is defined as the amount of drug a patient gets, such as 15 mg. These drugs have already been approved by the FDA for other types of cancer. This study tests different doses of the lenalidomide to see which dose is safer and more tolerable for people when combined with EPOCH chemotherapy. Another purpose of the study is genetic testing using tumor tissue to see if the combination of drugs may work in treating specific types of cancer. In addition, another objective of the study is to see how the combination of drugs affects HTLV levels and the number of immune cells in patients' blood. This is the first time all of these drugs will be tested together in patients with HTLV-associated adult T-cell leukemia-lymphoma (ATLL). There will be about 30 people taking part in this study.