Lenalidomide and Dexamethasone With or Without Thalidomide in Treating Patients With Multiple Myeloma

Inclusion Criteria: * Patients must be diagnosed with symptomatic multiple myeloma within the past 90 days confirmed by the following: * Bone marrow plasmacytosis with \>= 10% plasma cells or sheets of plasma cells or biopsy proven plasmacytoma which must be obtained within 4 weeks prior to randomization * Measurable levels of monoclonal protein (M protein): \>= 1.0 g/dL on serum protein electrophoresis or \>= 200 mg of monoclonal light chain on a 24 hour urine protein electrophoresis which must be obtained within 4 weeks prior to randomization; both serum protein electrophoresis (SPEP) and urine protein electrophoresis (UPEP) are required to be performed within 28 days prior to randomization; please note that if both serum and urine m-components are present, both must be followed in order to evaluate response * Hemoglobin \> 7 g/dL * Platelet count \> 75,000 cells/mm\^3 * Absolute neutrophil count \> 1000 cells/mm\^3 * Creatinine \< 2.5 mg/dL and creatinine clearance (measured or calculated) \>= 60 mL/min * Bilirubin =\< 1.5 mg/dL * Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) and serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) =\< 2.5 times the upper limit of normal * Prior palliative and/or localized radiation therapy is permitted provided at least 4 weeks have passed from date of last radiation therapy to date of registration; patients with prior solitary plasmacytoma treated with radiation thera…