Lenalidomide, Thalidomide and Dexamethasone in Treating Participants With Relapsed or Refractory Multiple Myeloma

Inclusion Criteria: * Understand and voluntarily sign an informed consent form * Relapsed/refractory multiple myeloma (MM) with measurable levels of myeloma paraprotein in serum (\>= 0.5 g/dl), urine (\>= 0.2 g excreted in a 24-hour collection sample), or abnormal free light chain (FLC) ratio * Serum creatinine =\< 2.5 mg/dl * Females of childbearing potential (FCBP)\* must have a negative serum or urine pregnancy test with a sensitivity of at least 50 mlU/mL within 10-14 days prior to and again within 24 hours of starting lenalidomide and must either commit to continued abstinence from heterosexual intercourse or begin TWO acceptable methods of birth control, one highly effective method and one additional effective method AT THE SAME TIME, at least 28 days before she starts taking lenalidomide. FCBP must also agree to ongoing pregnancy testing. Men must agree to use a latex condom during sexual contact with a female of childbearing potential even if they have had a successful vasectomy. All patients must be counseled at a minimum of every 28 days about pregnancy precautions and risks of fetal exposure. * A female of childbearing potential is a sexually mature woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months). * Absolute neutrophil count \> 1000 cells/mm\^3 * Platelet count \> 50,000 cells/mm\^3 for patients with \< 50% of bone marrow plasma cells and platelet count \> 25,000 cells/mm\^3 for patients in whom \> 50% of the bone marrow nucleated cells were plasma cells * Total bilirubin =\< 2.0 mg/dL * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) \< 3 x upper limit of normal (ULN) * Able to take prophylactic anticoagulation, warfarin or equivalent agent * Patient is able to understand and comply with the terms and conditions of the lenalidomide and thalidomide counseling program * All study participants must be registered into the mandatory RevAssist program, and be willing and able to comply with the requirements of RevAssist, AND the S.T.E.P.S. program Exclusion Criteria: * Any serious medical condition, or psychiatric illness that would prevent the subject from signing the informed consent form * Pregnant or breast feeding females. (Lactating females must agree not to breast feed while taking lenalidomide) * Use of any cancer therapy within 21 days prior to beginning cycle 1 day 1 of therapy (radiation therapy allowed within 5 days of completion of radiation therapy). * Known hypersensitivity to thalidomide, lenalidomide and dexamethasone. * The development of erythema nodosum if characterized by a desquamating rash while taking thalidomide or similar drugs.