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)