Inclusion Criteria:

* Patients must be diagnosed with asymptomatic high-risk smoldering multiple myeloma (SMM) within the past 12 months. High-risk is defined by the presence of 2 or more of the following factors:

* Abnormal serum free light chain ratio of involved to uninvolved \>20, but less than 100 if the involved FLC is \>= 10 mg/dL by serum free light chain (FLC) assay
* Serum M-protein level \>= 2 gm/dL
* Presence of t(4;14) or del 17p, del 13q or 1q gain by conventional cytogenetics or fluorescence in situ hybridization (FISH) studies.
* \>20% plasma cells on biopsy or aspirate
* Bone marrow aspirate and/or biopsy is required to be performed within 42 days prior to randomization and must demonstrate 10-59% clonal plasma cells.
* \>= 1 g/dL on serum protein electrophoresis (within 28 days prior to randomization).
* \>= 200 mg of monoclonal protein on a 24 hour urine protein electrophoresis (within 28 days prior to randomization).

* NOTE: In the rare situation where the serum protein electrophoresis (SPEP) is felt to be unreliable, then quantitative immunoglobulin levels on nephelometry or turbidometry can be accepted.
* SPEP, urine protein electrophoresis (UPEP), and serum FLC are required to be performed within 28 days prior to randomization.

* NOTE: 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 hour (hr), and urine in addition to serum must be followed in order to confirm a very good partial response (VGPR) or higher response.
* Patients must have no lytic lesions, no known plasmacytoma, and no unexplained hypercalcemia (i.e., \> 11 mg/dL or 1mg/dL above upper limit of normal \[ULN\]).
* Hemoglobin \>= 11 g/dL (within 28 days prior to randomization).
* Platelet count \>= 100,000 cells/mm\^3 (within 28 days prior to randomization).
* Absolute neutrophil count \>= 1500 cells/mm\^3 (within 28 days prior to randomization).
* Calculated creatinine clearance \>= 30 mL/min (within 28 days prior to randomization).
* Bilirubin =\< 1.5 mg/dL (within 28 days prior to randomization).
* 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 (within 28 days prior to randomization).
* Patients must not have any prior or concurrent systemic or radiation therapy for the treatment of myeloma. Patients must also not have contraindication to deep vein thrombosis (DVT) prophylaxis/aspirin.
* Patients must not have more than one focal marrow lesion on magnetic resonance imaging (MRI) of either pelvis or spine. Patients with indwelling pacemakers and/or ICD (implantable cardioverter-defibrillator) that is known or suspected to be MRI incompatible will be excused from this test.
* Concurrent use of erythropoietin is not allowed while on study therapy.
* Prior or glucocorticosteroid therapy for the treatment of multiple myeloma is not permitted. Prior systemic glucocorticosteroid use for the treatment of non-malignant disorders is permitted; concurrent use after registration on the study should be restricted to the equivalent of prednisone 10 mg per day. Prior or concurrent topical or localized glucocorticosteroid therapy to treat non-malignant comorbid disorders is permitted.
* Patients must not have active, uncontrolled seizure disorder. Patients must not have had a seizure in the last 6 months.
* Patients must not have uncontrolled intercurrent illness including uncontrolled hypertension, symptomatic congestive heart failure, unstable angina, uncontrolled cardiac arrhythmia, uncontrolled psychiatric illness or social situation that would limit compliance with the study, or a prior history of Stevens Johnson syndrome.
* Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status 0, 1, or 2.
* Patients with monoclonal gammopathy of undetermined significance are not eligible.
* Patients must not have grade 2 or higher peripheral neuropathy per CTCAE.
* Patients must not have active, uncontrolled infection.
* Patients may have a history of current or previous deep vein thrombosis or pulmonary embolism but are required to take some form of anti-coagulation as prophylaxis if they are not currently on full-dose anticoagulation.
* Patients should not have New York Heart Association classification III or IV heart failure at baseline.
* Patients with a history of prior malignancy are eligible provided they were treated with curative intent and have been free of disease for the time period considered appropriate for cure of the specific cancer. For most diseases this time frame is 5 years.
* Patients must agree to register into the mandatory Risk Evaluation and Mitigation Strategy (REMS) program and be willing and able to comply with the requirements of REMS.
* Women must not be pregnant due to potential harm to the fetus from daratumumab and lenalidomide. All females of childbearing potential (FCBP) must have a blood test or urine study with a sensitivity of at least 25 mIU/mL within 10-14 days prior to the first dose of lenalidomide and again within 24 hours prior to the first dose of lenalidomide. FCBP must also agree to ongoing pregnancy testing while on treatment. A female of childbearing potential is any woman, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy, or 3) has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months).
* Females of childbearing potential (FCBP) must either abstain from sexual intercourse for the duration of their participation in the study or agree to use TWO acceptable methods of birth control, one highly effective method and one additional effective method AT THE SAME TIME for 1) at least 28 days before starting study treatment; 2) while participating in the study; 3) during dose interruptions; and 4) for at least 28 days after the last dose of protocol treatment (FCBP who are assigned to Arm A and receive daratumumab must extend this contraception requirement to 3 months after the last dose of protocol treatment). Women must also agree to not breastfeed during this same time period. Men must agree to either abstain from sexual intercourse for the duration of their participation in the study or use a latex condom during sexual contact with a FCBP while participating in the study and for 28 days after the last dose of protocol treatment even if they have had a successful vasectomy. Men must also agree to abstain from donating sperm while on study treatment and for 28 days after the last dose of protocol treatment even if they have had a successful vasectomy. Both women and men must both agree to abstain from donating blood during study participation and for at least 28 days after the last dose of protocol treatment.
* Human immunodeficiency virus (HIV)+ patients with undetectable HIV viral loads tested within 6 months are eligible.
* Patients should not have a history of allergic reactions attributed to compounds of similar chemical or biologic composition to daratumumab, lenalidomide, or dexamethasone.
* Patients must not have known chronic obstructive pulmonary disease (COPD) with a forced expiratory volume in 1 second (FEV1) \<50% of predicted normal or known moderate or severe persistent asthma within 2 years prior to randomization