Lenalidomide, Dexamethasone, and Elotuzumab With or Without Cyclophosphamide in Treating Patients With Relapsed Primary Amyloidosis

Inclusion Criteria: * Biopsy-proven histochemical diagnosis of amyloid light-chain (AL) amyloidosis based on tissue specimens with Congo red staining or other histologic stain; thioflavin T or S, or crystal violet; tandem mass spec or immunohistochemistry (IHC) confirmation of immunoglobulin-derived amyloidosis is encouraged; cases in which histochemical confirmation is lacking need to be discussed with one of the Multiple Myeloma Research Foundation (MMRF) protocol chair/co-chairs * One prior line of therapy (defined as either one non-transplant regimen such as MelDex, Vel-Dex or CyBorD, one autologous stem cell transplant, or one regimen of non-transplant induction therapy followed by a single autologous stem cell transplant (without hematologic progression between induction and autologous stem cell transplant \[ASCT\]) * Measurable hematologic disease as defined by: * Serum differential free light chain concentration (dFLC, difference between amyloid forming \[involved\] and non-amyloid forming \[uninvolved\] free light chain \[FLC\]) \>= 50 mg/L) * Objective measurable (cardiac, renal or liver) organ amyloid involvement defined as follows (amyloid involvement of at least 1 required): * Mean wall thickness \> 12 mm on echocardiogram, with no other cardiac cause or an elevated NT-ProBNP (\> 332 ng/L) in the absence of renal failure or atrial fibrillation * Renal involvement is defined as proteinuria (predominantly albumin) \> 0.5 g/day in a 24-hour urine collection * Total liver span \> 15 cm in the absence of heart failure or alkaline phosphatase \> 1.5 times institutional upper limit of normal (ULN) * NOTE: Amyloid involvement of other organ systems is allowed, but not required * Life expectancy of \>= 6 months * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * . Female subjects who are of non-reproductive potential (i.e., post-menopausal by history for at least 24 consecutive months; OR history of hysterectomy; OR history of bilateral tubal ligation; OR history of bilateral oophorectomy).Female of child bearing potential (FCBP) must have a negative serum or urine pregnancy test with a sensitivity of at least 25 mIU/mL or equivalent units of human chorionic gonadotropin (hCG) within 10 ? 14 days prior to and again within 24 hours of starting lenalidomide and study drug and must either commit to continue 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 4 weeks before she starts taking lenalidomide through 4 weeks after the last dose of lenalidomide and 5 half-lives after elotuzumab plus 30 days (duration of ovulatory cycle) for a total of 180 days post-last dose of elotuzumab; FCBP must also agree to ongoing pregnancy testing during the entire duration of treatment. Males must agree to use a latex or synthetic condom during sexual contact with a FCBP even if they have had a vasectomy from the time of signing the informed consent form through 28 days after the last dose of lenalidomide and 5 half-lives of elotuzumab plus 90 days (duration of sperm turnover) for a total of 180 days post-last dose of elotuzumab; these same patients must not donate sperm; all patients must be counseled at a minimum of every 28 days about pregnancy precautions and risks of fetal exposure; all patients prior to taking lenalidomide, must be registered in and must comply with all requirements of the lenalidomide Risk Evaluation and Mitigation Strategies (REMS) program * Ability to understand the purpose and risks of the study and provide signed and dated informed consent and authorization to use protected health information * Absolute neutrophil count (ANC) \>= 1,000 cells/mm\^3 (1.0 x 10\^9/L) * Platelet count \>= 75,000 cells/mm\^3 (75 x 10\^9/L) * Hemoglobin \>= 8.0 g/dl (red blood cell \[RBC\] transfusions are permitted) * Total bilirubin =\< 1.5 x ULN (except if the patient has Gilbert?s syndrome who can have total bilirubin =\< 2 x ULN) * Alkaline phosphatase =\< 5 x ULN * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransaminase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3.0 x ULN * Renal function: creatinine clearance by Cockcroft-Gault formula \>= 30 mL/min Exclusion Criteria: * Amyloidosis due to mutations of the transthyretin gene or presence of other non-AL amyloidosis; exception: patients with amyloid heavy (AH) or mixed AL/AH type amyloidosis are potentially eligible * Peripheral neuropathy \>= grade 3 sensory neuropathy or \>= grade 2 sensory neuropathy with pain within 14 days of registration; prior neuropathy of this severity improved due to medical management such as gabapentin are potentially eligible * Cardiac stage 2 or 3 with N-terminal prohormone (NT-pro)-B-type natriuretic peptide (BNP) \> 8500 ng/L * Medically documented cardiac syncope, uncompensated New York Heart Association (NYHA) class 3 or 4 congestive heart failure, myocardial infarction within the previous 6 months, unstable angina pectoris, uncontrolled hypertension (defined as an average systolic blood pressure \[SBP\] over 140 or a diastolic blood pressure \[DBP\] over 90 despite antihypertensive agents), clinically significant repetitive ventricular arrhythmias despite antiarrhythmic treatment, or severe orthostatic hypotension or clinically important autonomic disease; prior to study entry, any electrocardiogram (ECG) abnormality at screening has to be documented by the investigator as not medically relevant; NOTE: there is no lower limit of left ventricular ejection fraction below which patients are excluded from participation * Any medical conditions that, in the investigator?s opinion, would impose excessive risk to the patient or would adversely affect his/her participating in this study, including: * Known active infection requiring parenteral anti-infective treatment at the time of initiation of treatment * Other malignancy diagnosed or requiring treatment within the past 3 years with the exception of adequately treated basal cell carcinoma, squamous cell skin cancer, carcinoma in-situ of the cervix or breast, or low-risk Gleason grade =\< 6 localized prostate cancer not requiring therapy * Pregnant or breast-feeding females * Serious psychiatric illness, active alcoholism, or drug addiction that may hinder or confuse compliance or follow-up evaluation * Known or active human immunodeficiency virus (HIV) infection or active hepatitis B or C viral infection * Cerebrovascular accident (CVA) with persistent neurologic deficits occurring within 6 months prior to enrollment; persisting neurologic deficits from a CVA occurring over 6 months prior to enrollment are not necessarily grounds for exclusion * Concurrent multiple myeloma (defined according to 2015 International Myeloma Working Group \[IMWG\] guidelines) * POEMS syndrome (plasma cell dyscrasia with polyneuropathy, organomegaly, endocrinopathy, monoclonal protein \[M-protein\] and skin changes) * Previous cytotoxic therapies, including cytotoxic investigational agents, within 3 weeks (6 weeks nitrosoureas) prior to start of study treatment; previous corticosteroids used with intent to treat amyloidosis within three weeks; (prednisone up to but no more than 10 mg orally once a day \[q.d.\] or its equivalent for symptom management of comorbid conditions is permitted but dose should be stable for at least 7 days prior to study treatment) * Residual side effects to previous therapy \> grade 1 prior to initiation of therapy (alopecia any grade and/or neuropathy grade 2 without pain are permitted) * Prior autologous or allogeneic stem cell transplant within 12 weeks of initiation of therapy * Prior allogeneic stem cell transplant within 16 weeks of initiation of therapy, or at any time if patient has active graft-versus-host-disease (GVHD) * Prior major surgical procedure or radiation therapy within 4 weeks of the first dose of study treatment (this does not include limited course of radiation used for management of bone pain within 7 days of first dose of study therapy) * Known intolerance to steroid therapy (defined as being unable to tolerate at least 20 mg dex/week) * Inability to tolerate prophylactic anti-thrombotic therapy * \>= grade 3 thromboembolic event in the last 6 months