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

* 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 \<=2, or \<= 3 if the decreased performance status is deemed to be due to disease and not residual toxicity from prior therapy or other causes. * Adequate organ and marrow function as defined below: * Absolute neutrophil count \>= 1,000/mcL * Platelets \>= 75,000/mcL * Total bilirubin \<= 1.5 X institutional upper limit of normal (ULN) * Aspartate aminotransferase (AST) serum glutamic-oxaloacetic transaminase (SGOT)/alanine aminotransferase (ALT) serum glutamic pyruvic transaminase (SGPT) \<= 2.5 X institutional upper limit of normal (ULN) * Serum Creatinine \<= 1.5 mg/dL OR * Creatinine Clearance \>= 60 mL/min/1.73 m\^2 as calculated by direct measurement of 24-hour urine for creatinine clearance * Negative serum or urine pregnancy test at screening for women of childbearing potential (WOCBP) NOTE: WOCBP is defined as any female who has experienced menarche and who has not undergone successful surgical sterilization or who is not postmenopausal. WOCBP must have a negative pregnancy test (hemoglobin (HCG) blood or urine) during screening. * All study participants must be registered into the mandatory Revlimid REMS(R) program and be willing and able to comply with the requirements of the Risk Evaluation and Mitigation Strategy (REMS(R) program. * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for at least 6 months after completion of treatment for women, and for at least 3 months after completion of treatment for men. Females of reproductive potential must adhere to the scheduled pregnancy testing as required in the Revlimid REMS(R) program. * Ability of subject to understand and the willingness to sign a written informed consent document. EXCLUSION CRITERIA: * Patients who are receiving any other investigational agents. * Anti-cancer treatment within 2 weeks prior to enrollment. (4 weeks for monoclonal antibodies and 6 weeks for nitrosoureas or mitomycin C). * Patients who have received two of the following drugs at any point: lenalidomide, romidepsin, and 5-azacitidine. Patients who have received only one of the three drugs remain eligible. * Patients with a diagnosis of cutaneous T-cell lymphoma (CTCL) are excluded from participation in the expansion cohort. * Other malignancy that requires ongoing systemic hormonal therapy, chemotherapy, or immunotherapy. * History of allergic reactions or known or suspected hypersensitivity attributed to compounds of similar chemical or biologic composition to lenalidomide, romidepsin and 5-azacitidine * Patients with uncontrolled intercurrent illness including, but not limited to, ongoing or active infection requiring systemic therapy, or psychiatric illness/social situations that would limit compliance with study requirements. * Human immunodeficiency virus (HIV)-infected patients on effective antiretroviral therapy with undetectable viral load within 6 months are eligible for this trial. * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. * Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load. * History of inflammatory bowel disease (e.g., Crohn's disease, ulcerative colitis), celiac disease (i.e., sprue), prior gastrectomy or upper bowel removal, or any other gastrointestinal disorder or defect that would interfere with the absorption, distribution, metabolism or excretion of the study drug and/or predispose the subject to an increased risk of gastrointestinal toxicity. * Clinically significant (i.e., active) cardiovascular disease: cerebral vascular accident/stroke (\< 6 months prior to enrollment), myocardial infarction (\< 6 months prior to enrollment), unstable angina, congestive heart failure (\>= New York Heart Association Classification Class II), congenital long QT syndrome, or other serious cardiac arrhythmia including 2nd degree atrio ventricular (AV) block type II, 3rd degree AV block, or bradycardia (ventricular rate less than 50 beats/min). * Hypertrophic cardiomegaly or restrictive cardiomyopathy from prior treatment or other causes. * Uncontrolled hypertension, i.e., blood pressure (BP) of \>=160/95; patients who have a history of hypertension controlled by medication must be on a stable dose (for at least one month) and meet all other inclusion criteria. * Triplicate average baseline QT corrected for heart rate by Fridericia's (QTcF) interval \>= 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.