Melphalan, Prednisone, and Thalidomide or Lenalidomide in Treating Patients With Newly Diagnosed Multiple Myeloma

Inclusion Criteria: * Patients must have a confirmed diagnosis of symptomatic myeloma; for the original diagnosis of myeloma patients should have met the following criteria at one point in their disease course: * Bone marrow plasmacytosis with \>= 10% plasma cells or sheets of plasma cells or biopsy proven plasmacytoma * Patient must have had symptomatic disease at initial diagnosis that prompted the initiation of therapy as well as evidence of end-organ damage at the time of diagnosis namely; at least one of the following: anemia, hypercalcemia, bone disease (lytic bone lesions or pathologic fracture), or renal dysfunction * NOTE: Patients with asymptomatic smoldering myeloma (serum m protein \>= 3 gm/dL or bone marrow plasma cells \>= 10% or greater plus no evidence of anemia, hypercalcemia, lytic bone lesions or renal dysfunction) and monoclonal gammopathy of undetermined significance (serum m protein \< 3 gm/dL and bone marrow plasma cells \< 10% plus no evidence of anemia, hypercalcemia, lytic bone lesions or renal dysfunction) are not eligible * Patients must be \> 65 and have declined alternative treatment OR patients who are \>= 18 \< 65 are eligible if they: * Are not a candidate for autologous stem cell transplantation in the opinion of the treating physician OR * Have declined transplant or other alternative treatment * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * All tests below must be performed within 28 days prior to randomization: * Serum free light chain assay * Kappa free light chain * Lambda free light chain * NOTE: The serum free light chain test is required to be done if the patient does not have measurable disease in the serum or urine; measurable disease in the serum is defined as having a serum M-spike \>= 1 g/dL; measurable disease in the urine is defined as having a urine M-spike \>= 200 mg/24 hr * NOTE: urine protein electrophoresis (UPEP) (on a 24 hour collection) is required, no substitute method is acceptable; urine must be followed monthly if the baseline urine M-spike is \>= 200 mg/24 hr; 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 * Total 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 * Patients must be previously untreated for myeloma, although prior treatment for myeloma with prednisone or dexamethasone for less than 4 weeks total dosing alone or in combination with thalidomide or lenalidomide for less than 2 weeks total dosing is allowable * Patients may be receiving bisphosphonates or growth factors (erythropoietin) for multiple myeloma; although erythropoietin is allowed, it is strongly discouraged due to increased risk of thrombosis when employed alongside thalidomide and/or lenalidomide therapy * Patients must be willing and able to take prophylaxis with either aspirin at 325 mg/day or alternative prophylaxis with either low molecular weight heparin or Coumadin * Females of childbearing potential (FCBP) must have a negative serum or urine pregnancy test with a sensitivity of at least 25 mIU/mL within 10 - 14 days and again within 24 hours prior to starting cycle 1 of lenalidomide; further, they 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 starting lenalidomide; FCBP must also agree to ongoing pregnancy testing; men must agree to use a latex condom during sexual contact with a FCBP, even if they have had a successful vasectomy; a FCBP 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); all patients must be counseled by a trained counselor every 28 days about pregnancy precautions and risks of fetal exposure * Patients must not have uncontrolled inter-current illness that would limit compliance with the study including: * Uncontrolled hypertension * Symptomatic congestive heart failure * Unstable angina * Uncontrolled cardiac arrhythmia * Uncontrolled psychiatric illness or social situation * Prior history of Stevens Johnson syndrome * Patients must not have grade 2 or higher peripheral neuropathy * Patients must not have an active, uncontrolled infection * Female patients MUST NOT be pregnant or breastfeeding; the use of these drugs in this patient population is ABSOLUTELY CONTRAINDICATED; for women of childbearing potential, a negative serum pregnancy test is required within 10-14 days prior to randomization; for female patients of childbearing potential a negative serum pregnancy test must be repeated within 24 hours prior to initiation of treatment, weekly for the first 4 weeks of treatment and then every 4 weeks if the patient's periods are regular or every 2 weeks if they are not; women of childbearing potential must be willing to refrain from sexual intercourse or must be willing to employ a dual method of contraception, one of which is highly effective \[intrauterine device (IUD), birth control pills, tubal ligation or partner's vasectomy\] and another additional method (condom, diaphragm or cervical cap) starting 4 weeks prior to and while taking lenalidomide and thalidomide and for four weeks after discontinuing this therapy; the male partner of a female using a single form of birth control should use a condom regardless of his vasectomy status * Sexually active males must be willing to use a condom (even if they have undergone a prior vasectomy) while having intercourse with any woman, while taking lenalidomide and thalidomide and for 4 weeks after stopping treatment * Patients must not have had a second active malignancy requiring treatment within the last 2 years, with the exceptions of basal or squamous cell carcinoma of the skin, in situ carcinoma of the cervix