Brentuximab Vedotin and Lenalidomide in Treating Patients With Relapsed or Refractory T-Cell Lymphomas

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Registered into mandatory Revlimid Risk Evaluation and Mitigation Strategies (REMS) program * Women of childbearing potential: adhere to scheduled pregnancy testing as required in the Revlimid REMS program * Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 * Histologically confirmed cutaneous T-cell non-Hodgkin lymphoma (CTCL) per World Health Organization (WHO) classification 2016 including, mycosis fungoides (MF) or Sezary syndrome (SS); phase 1 : \>= stage IIB OR \>= stage IB-IIA folliculotropic/transformed MF; expansion cohort: \>= stage IB * MF/SS stage of disease according to TNMB classification * SS is defined as meeting T4 plus B2 criteria; where the biopsy of erythrodermic skin may only reveal suggestive but not diagnostic histopathologic 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 been recommended by the International Society for Cutaneous Lymphomas (ISCL) should be used * Relapsed/refractory disease * Failed \>= 2 prior systemic therapies * CD30-positivity by immunohistochemistry of \>= 1% * Measurable disease per modified Severity Weighted Assessment and/or Sezary count * Fully recovered from acute toxicities (except alopecia) of all prior therapies to Common Terminology Criteria for Adverse Events (CTCAE) =\< grade 1 * May have received either brentuximab vedotin or lenalidomide/immunomodulatory imide drugs (IMiD) without dose modification/delay due to toxicity \* IMiDs defined as thalidomide analogues * If received prior brentuximab vedotin or lenalidomide, must be able to tolerate the dose level to which the participant will be enrolled to * Within 14 days prior to day 1 of protocol therapy unless otherwise stated: Absolute neutrophil count (ANC) \>= 1,000/mm\^3 \* NOTE: Growth factor is not permitted within 14 days of ANC assessment unless cytopenia is secondary to disease involvement * Within 14 days prior to day 1 of protocol therapy unless otherwise stated: Platelets \>= 75,000/mm\^3 \* NOTE: Platelet transfusions are not permitted within 14 days of platelet assessment unless cytopenia is secondary to disease involvement * Within 14 days prior to day 1 of protocol therapy unless otherwise stated: Total bilirubin =\< 1.5 X upper limit of normal (ULN) OR if Gilbert's syndrome =\< 3.0 X ULN * Within 14 days prior to day 1 of protocol therapy unless otherwise stated: Aspartate aminotransferase (AST) =\< 2 x ULN * Within 14 days prior to day 1 of protocol therapy unless otherwise stated: Alanine aminotransferase (ALT) =\< 2 x ULN * Within 14 days prior to day 1 of protocol therapy unless otherwise stated: Creatinine clearance of \>= 60 mL/min per 24 hour urine test or the Cockcroft-Gault formula * Within 14 days prior to day 1 of protocol therapy unless otherwise stated: Women of childbearing potential (WOCBP): 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 * Agreement by WOCBP and males of childbearing potential to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 6 months after the last dose of protocol therapy \* Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only) Exclusion Criteria: * Stem cell transplantation * Monoclonal antibody within 28 days prior to day 1 of protocol therapy * Any systemic therapy, including monoclonal antibody within 28 days or 5 half-lives (whichever is shorter) of initiating day 1 of protocol therapy * Any skin-directed therapy within 14 days prior to day 1 of protocol therapy * Any radiation therapy within 21 days prior to day 1 of protocol therapy * Immunosuppressive medication within 14 days prior to day 1 of protocol therapy; 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 day 1 of protocol therapy * Disease free of prior malignancies for \>= 5 years with the exception of: * Currently treated squamous cell and basal cell carcinoma of the skin, or * 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 lenalidomide or history of anaphylactic shock to brentuximab vedotin in the past * Female only: pregnant or breastfeeding * Acute infection requiring systemic treatment * Known history of human immunodeficiency virus (HIV) infection * Active hepatitis B or C infection * Central nervous system involvement by lymphoma, including leptomeningeal involvement * History of progressive multifocal leukoencephalopathy (PML) * Current peripheral neuropathy \>= grade 2 or patients with the demyelinating form of Charcot-Marie-Tooth syndrome * 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 * History of vascular disease (e.g. deep vein thrombosis, stroke) * Major surgery (as defined by the investigator) within the 28 days prior to day 1 of protocol therapy * Incidence of gastrointestinal disease that may significantly alter the absorption of lenalidomide * Any other condition that would, in the investigator's judgment, 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. * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)