Romidepsin, CC-486 (5-azacitidine), Dexamethasone, and Lenalidomide (RAdR) for Relapsed/Refractory T-cell Malignancies

Background: Mature T-cell malignancies (TCMs) are a rare group of cancers that usually do not have effective treatments or cures. Because of this, participants with TCMs often relapse and have a poor overall prognosis. This trial is testing if combining several drugs against TCMs can be a more effective. Primary Objective: To test if the combination of romidepsin, CC-486 (5-azacitidine), dexamethasone, and lenalidomide (RAdR) can be given safely to participants with relapsed or treatment refractory TCM. Other (Secondary) Objective: Measure the activity of this combination treatment. Eligibility: People age 18 and older who have a failed or relapsed after standard treatments for mature TCMs. Design: Participants will be screened for eligibility by performing the following tests or procedures: Physical exam Medical history Medicine review Blood and urine tests Symptom review Bone marrow examination Total Body imaging scans or x-rays Tumor biopsy Participants will have blood tests during treatment to make sure their blood cell counts are okay. Romidepsin is infused through an intravenous (IV) placed in one of the veins usually in the arm. Lenalidomide, dexamethasone, and CC-486 (5-azacitidine) are pills or capsules taken by mouth. Participants are asked to keep a diary of when they take their pills to make sure they are taking these medicines properly. Participants will have tumor imaging scans after every 2nd cycle (or 6 weeks) to check if the treatment is working. If the doctors are concerned the cancer has spread to the brain and/or spine, they will have scans of the area(s) and a sampling of the fluid around the brain/spine which is obtained through a small needle inserted into the lower part of the back for a short time to collect the fluid. This procedure is called a spinal tap or lumbar puncture. Participants who have tumor in their skin will have repeat exams of their skin and sometimes photographs taken of these areas to see if the treatment is working. Participants will also be asked to give blood, saliva, and sometimes have optional biopsies of their tumor where these tests are done for research purposes. After they have completed the protocol treatment (6 cycles), they will be asked to return to clinic 30 days after treatment has ended, then every other month (or 60 days) for the first 6 months, then every 3 months (90 days) for 2 years, and then every 6 months for years 2 to 4 after completing treatment. After 4.5 years, they will be seen once a year.

* INCLUSION CRITERIA: * Patients must have relapsed after or progressed during at least one line of prior systemic therapy (which may include allogeneic stem cell transplantation) for mature T or NK/T neoplasm, i.e. have relapsed and/or refractory mature T and natural killer (NK) neoplasm per 2016 World Health Organization (WHO) classification excluding chronic lymphoproliferative disorder of NK cells, aggressive NK-cell leukemia, and Cutaneous T-Cell Lymphoma. * T or NK/T neoplasm from initial diagnosis or recurrence must be histologically or cytologically proven and diagnosis be confirmed by the Laboratory of Pathology, National Cancer Institute (NCI), * Patients with anaplastic large cell lymphoma (ALCL) or cluster of differentiation (CD30) positive mycosis fungoides (MF) or Sézary syndrome (SS) must have relapsed after or become intolerant to prior anti-CD30 targeting therapy treatment with brentuximab vedotin * For patients without circulating leukemia/lymphoma cells detectable by flow cytometry, a formalin fixed tissue block or 15 slides of tumor sample (archival or fresh) must be available at enrollment for performance of correlative studies. NOTE: Patients without circulating malignant cells must be willing to have a tumor biopsy if prior tissue or adequate archival tissue is not available (i.e., post-enrollment and prior to treatment). * Disease must be measurable with at least one measurable lesion by response evaluation criteria in lymphoma (RECIL) 2017 or Modified Severity-Weighted Assessment Tool (mSWAT) criteria, or have an abnormal clonal T-cell population detectable by peripheral blood flow cytometry * Age \>18 years * Eastern Cooperative Oncology Group (ECOG) performance status \= 75,000/mcL * Total bilirubin \= 480 ms * Patients taking drugs leading to significant QT prolongation Note: A 5 half-life washout period must have elapsed following the use of these drugs prior to administration of romidepsin. * Concomitant use of rifampin and other strong cytochrome P450 3A4 (CYP3A4) inhibitors and inducers within 2 weeks prior to starting protocol therapy. * Other severe acute or chronic medical conditions including psychiatric conditions such as recent (within the past year) or active suicidal ideation or behavior; or laboratory abnormalities that may increase the risk associated with study participation or study treatment administration or may interfere with the interpretation of study results and, in the judgment of the investigator, would make the patient inappropriate for entry into this study. * Pregnant or lactating women. Pregnant women are excluded from this study because lenalidomide is a Class X agent with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with lenalidomide, breastfeeding should be discontinued if the mother is treated with lenalidomide. These potential risks may also apply to other agents used in this study.