Durvalumab With or Without Lenalidomide in Treating Patients With Relapsed or Refractory Cutaneous or Peripheral T Cell Lymphoma

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Registered into Revlimid REMS program * Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 * Fully recovered from acute toxicities (except alopecia) of all prior therapies to Common Terminology Criteria for Adverse Events (CTCAE) =\< grade 1 * Relapsed/refractory disease * Failed \>= 2 prior systemic therapies \*NOTE: For systemic ALCL prior systemic therapy must also include progression on brentuximab vedotin CUTANEOUS T-CELL LYMPHOMA (CTCL) ONLY * Histologically confirmed mycosis fungoides (MF) or Sezary syndrome (SS); Phase 1: \>= stage IIB OR \>= stage IB-IIA folliculotropic/transformed MF; Phase 2: \>= stage IB * Stage of disease according to TNMB classification * Pathology report must be diagnostic or be consistent with MF/SS criteria * SS is defined as meeting T4 plus B2 criteria; where the biopsy of erythrodermic skin may only reveal suggestive but not diagnostic histopathological features, the diagnosis may be based on either node biopsy or fulfillment of B2 criteria * For MF where the histological diagnosis by light microscopic examination is not confirmed, diagnostic criteria that has been recommended by the International Society of Cutaneous Lymphomas (ISCL) should be used * Measurable disease per modified severity weighted assessment tool (mSWAT) and/or Sezary count * Baseline skin biopsy taken within 6 months available for central review submission PERIPHERAL T-CELL LYMPHOMA (PTCL) ONLY * Histologically confirmed PTCL as defined by World Health Organization (WHO) 2008 criteria * Measurable and/or evaluable disease per Lugano Classification * Absolute neutrophil count (ANC) \>= 1000/mm\^3 \* Growth factor is not permitted within 14 days of ANC assessment unless cytopenia is secondary to disease involvement * Platelets \>= 100,000/mm\^3 \* Platelet transfusions are not permitted within 14 days of platelet assessment unless cytopenia is secondary to disease involvement * Total serum bilirubin =\< 2.2 mg/dL * Aspartate aminotransferase (AST) =\< 2 x upper limit of normal (ULN) * Alanine aminotransferase (ALT) =\< 2 x ULN * Creatinine clearance of \>= 60 mL/min per the Cockcroft-Gault formula * If not receiving anticoagulants: international normalized ratio (INR) AND prothrombin (PT) =\< 1.5 x ULN \* If on anticoagulant therapy: PT must be within therapeutic range of intended used of anticoagulants * Female of childbearing potential: negative urine or serum pregnancy test \* If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Female of child bearing potential: willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 90 days after the last dose of study medication \* Childbearing potential defined as not being surgically sterilized or have not been free from menses for \> 1 year * Male: use an adequate method of contraception starting with the first dose of study therapy through 90 days after the last dose of study therapy Exclusion Criteria: * Immunotherapy with immune checkpoint inhibitors, cell-based therapies, or cancer vaccines * Lenalidomide, thalidomide or other immunomodulatory drugs (IMiDs) * Monoclonal antibody within 5 half-lives of the antibody prior to initiating protocol therapy * Any systemic therapy, including monoclonal antibody within 28 days or 5 half-lives (whichever is shorter) of initiating protocol therapy * Any skin-directed therapy within 14 days prior to initiating protocol therapy * Any radiation therapy within 21 days prior to initiating protocol therapy * Immunosuppressive medication within 14 days prior to the first dose of study treatment; the following are exceptions to this criterion: * Intranasal, inhaled, topical or local steroid injections (e.g., intra-articular injection) and are on stable dose for at least 28 days * Systemic corticosteroids at physiologic doses of \< 10 mg/day of prednisone or equivalent * Live, attenuated vaccine within 30 days prior to the first dose of protocol therapy * History of pneumonitis (non-infectious) that required steroids or current pneumonitis * Disease free of prior malignancies for \>= 5 years with the exception of: * Currently treated squamous cell and basal cell carcinoma of the skin * Carcinoma in situ of the cervix, or * Surgically removed melanoma in situ of the skin (stage 0) with histological confirmed free margins of excision or * Prostate cancer (T1a or T1b using the TNM \[tumor, nodes, metastasis\] clinical staging system) that has/have been surgically cured, or * Any other malignancy that has/have been curatively treated with surgery and/or localized radiation * Allergic reaction/ hypersensitivity to thalidomide or to the excipients contained in the formulation of durvalumab * Female only: pregnant or lactating * Prior stem cell transplantation * Acute infection requiring systemic treatment * Known history of human immunodeficiency virus (HIV) infection * Active hepatitis B or C infection * Conditions requiring chronic steroid or immunosuppressive treatment that likely need additional steroid or immunosuppressive treatments in addition to the protocol therapy * Current peripheral neuropathy \>= grade 2 * Renal failure requiring hemodialysis or peritoneal dialysis * Unstable cardiac disease as defined by one of the following: * Cardiac events such as myocardial infarction (MI) within the past 6 months * NYHA (New York Heart Association) heart failure class III-IV * Uncontrolled atrial fibrillation or hypertension * Major surgery (as defined by the investigator) within the 28 days prior to the first dose of study treatment * Active or prior documented autoimmune or inflammatory disorders requiring therapy within the past 3 years prior to the start of treatment; the following are exceptions to this criterion: * Vitiligo or alopecia; * Hypothyroidism (e.g., following Hashimoto syndrome) stable on hormone replacement; or * Psoriasis not requiring systemic treatment * History of primary immunodeficiency * Incidence of gastrointestinal disease that may significantly alter the absorption of lenalidomide * Any other condition that would, in the investigator's judgement, contraindicate the patient's participation in the clinical study due to safety concerns or compliance with clinical study procedures, e.g., infection/inflammation, intestinal obstruction, unable to swallow medication, social/psychological issues, etc * In the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)