Lenalidomide and Dexamethasone With or Without Anakinra in Treating Patients With Early Stage Multiple Myeloma

Inclusion Criteria: * Absolute neutrophil count (ANC) \>= 1700/mm\^3 * Platelet count \>= 100,000/mm\^3 * Hemoglobin \>= 8.0 g/dL * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) =\< 3 x upper limit of normal (ULN) * Creatinine clearance \>= 30 mL/min (as determined by Cockroft-Gault equation) * Diagnosis of multiple myeloma according to International Myeloma Working Group criteria and one of the following: * Smoldering multiple myeloma (SMM) * Indolent multiple myeloma (IMM) * Newly diagnosed multiple myeloma (MM) * Note: patients with lytic disease and anemia are eligible * High risk disease defined by all of the following: * \>= 10% bone marrow plasma cells AND * Abnormal serum free light chain (FLC) ratio (\< 0.26 or \> 1.65) by serum FLC assay AND * Monotypic plasma cell S-phase \>= 0.3% * Measurable level of M-protein \> 1 g/dL on serum protein electrophoresis or \> 200 mg of M-protein on a 24 hour urine protein electrophoresis * Negative tuberculosis (TB) testing (Quantiferon - TB blood test or skin test) =\< 7 days prior to registration * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2 * Provide signed informed consent * Negative (serum or urine) pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only; NOTE: a second pregnancy test must be performed within 24 hours prior to the start of lenalidomide; the subject may not receive lenalidomide until the study doctor has verified that the results of these pregnancy tests are negative * Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study) * Willing and able to comply with the requirements of the Revlimid Risk Evaluation and Mitigation Strategy (REMS) program * Females of childbearing potential must be willing to adhere to the scheduled pregnancy testing as required by the Revlimid REMS program Exclusion Criteria: * Prior treatment with any other agent that may affect M-protein =\< 30 days prior to registration * Acute/chronic infections, open wounds, or any active infection requiring intravenous antibiotic therapy =\< 12 weeks prior to registration * Other active malignancy (=\< 3 years) prior to registration; exceptions: basal cell skin cancer or carcinoma-in-situ of the cervix or low-risk prostate cancer after curative therapy * Any of the following: * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception * New York Heart Association (NYHA) class 3 or 4 congestive heart failure (CHF) symptoms * Other concurrent chemotherapy, radiotherapy, or any ancillary therapy considered investigational; NOTE: bisphosphonates are allowed while on protocol treatment