Dalteparin, Lenalidomide, and Low-Dose Dexamethasone in Treating Patients With Previously Untreated Multiple Myeloma

Inclusion Criteria: * Patients must have a diagnosis of active MM requiring treatment, as diagnosed by a bone marrow biopsy within 8 weeks prior to study enrollment * Patients must not have received any previous treatment for MM (localized radiation therapy or single agent pulse steroid therapy for acute MM crises is permitted) * Life expectancy of greater than 12 weeks * Eastern Cooperative Oncology Group (ECOG) performance status \< 2 (Karnofsky \>= 50%) * Total bilirubin \< 1.5 x upper limit of normal (ULN) * Transaminases (aspartate aminotransferase \[AST\]/alanine aminotransferase \[ALT\]) \< 2.5 x ULN * Alkaline phosphatase \< 2.5 ULN * Platelets \>= 75,000 cells/mm3 * Hemoglobin \>= 8.0 g/dL * Absolute neutrophil count (ANC) \> 1,000 cells/mm3 NOTE: Patients with platelet count \< 75,000 or hemoglobin \< 8.0 g/dl,or ANC \<1,000 cell/mm3 secondary to extensive bone marrow disease can be enrolled at Principal Investigator's (PI) discretion with appropriate transfusion and/or cytokine support * Creatinine =\< 2.5 mg/dL (=\< 200 mmol/L) or creatinine clearance \> 30 ml/min (as calculated by the Cockcroft-Gault formula) * Females of childbearing potential (FCBP) must have a negative serum or urine pregnancy test with a sensitivity of at least 50 mIU/mL within 10-14 days and again within 24 hours prior to prescribing lenalidomide for Cycle 1 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 FCBP even if they have had a successful vasectomy * All study participants must be registered into the mandatory RevAssist program, and be willing and able to comply with the requirements of RevAssist * Willingness and ability to sign informed consent for the clinical trial Exclusion Criteria: * Patients who have had any prior chemotherapy for MM; with the exception of pulse steroids for any myeloma-related acute events * Other concurrent chemotherapy, immunotherapy, radiotherapy, or any ancillary therapy considered investigational * Pregnant or lactating women * Active serious infections uncontrolled by antibiotics at the time of treatment initiation * Inability to give voluntary written informed consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care * Failure to comply with birth control methods as described above * Any serious medical or psychiatric condition or reason that, in the PI's opinion, makes the patient unsuitable to participate in this clinical trial * Known to be human immunodeficiency virus (HIV) positive (if the status of HIV is not known and patient is not at risk, as determined by the PI, then the patient will not be specifically tested for HIV); HIV-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with lenalidomide and/or dalteparin. In addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy * Diagnosed or treated for another malignancy within 3 years of enrollment, with the exception of complete resection of basal cell carcinoma or squamous cell carcinoma of the skin, an in situ malignancy, or low-risk prostate cancer (organ-confined, early stage disease) after curative therapy * Patients with M protein \>6 gm/dl prior to starting treatment will be excluded from the initial "run-in" cohort on both arms of the study, but will be eligible for the subsequent enrollment of patients who do not have a run-in phase with dalteparin