Phase 1-2 Amrubicin in Combo With Lenalidomide + Weekly Dexamethasone in Relapsed/Refractory Multiple Myeloma

Inclusion Criteria: * Relapsed or refractory multiple myeloma that has progressed following at least 1 prior therapy. * Measurable disease defined as one of the following: * Serum M-protein ≥ 1 g/dL * Urine M-protein ≥ 200 mg/24 hours * Received at least 1 prior line of systemic treatment that may have included lenalidomide and/or an anthracycline. * No cytotoxic chemotherapy within 4 weeks prior to first dose of amrubicin. This interval may be reduced to 14 days for thalidomide, lenalidomide, bortezomib or corticosteroids, provided other entry criteria are met. * Age ≥ 18 at the time of consent. * Life expectancy of more than ≥ 3 months. * No known central nervous system involvement by myeloma. * Eastern Cooperative Oncology Group (ECOG) performance status 0 to 1 at study registration during phase 1. Once safety is confirmed, ECOG performance status 0 to 2 at study registration during phase 2. * No poorly-controlled intercurrent illness. * Platelets \> 100 x 10\^9/L * Hemoglobin \> 8.0g/dL * Absolute neutrophil count (ANC) \>1.5 x 10\^9/L * Aspartate transaminase (AST) and alanine transaminase (ALT) ≤ 3 x upper limit of normal (ULN) * Total bilirubin ≤ 1.5 x ULN * Calculated creatinine clearance ≥ 50 mL/min by Cockcroft-Gault formula. * Left ventricular ejection fraction (LVEF) ≥ 50% by Echocardiogram (ECHO) or multiple gate acquisition scan (MUGA) * All study participants must be registered into the mandatory RevAssist program, and be willing and able to comply with the Requirements of RevAssist. * Disease-free of prior malignancies for ≥ 5 years with exception of currently treated basal cell, squamous cell carcinoma of the skin, or carcinoma "in situ" of the cervix or breast. * Females of childbearing potential (FCBP) must have a negative serum or urine pregnancy test with a sensitivity of at least 50 U/mL within 10 to 14 days and again within 24 hours prior to prescribing lenalidomide for Cycle 1 (prescriptions must be filled within 7 days) and must either commit to continued abstinence from heterosexual intercourse or begin 2 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. * Ability to understand and the willingness to sign a written informed consent document. * Able to adhere to the study visit schedule and other protocol requirements. * Able to take aspirin (81 or ≥ 25 mg) daily as prophylactic anticoagulation. Patients intolerant to aspirin may use warfarin or low molecular weight heparin (LMWH). Patients with previous thromboembolic event on lenalidomide or thalidomide may be started on warfarin or LMWH. Patients already taking warfarin or LMWH do not require additional aspirin.. * Lactating females must agree not to breast-feed while taking lenalidomide Exclusion Criteria: * Any serious medical condition, laboratory abnormality, or psychiatric illness that would prevent the subject from signing the informed consent form. * Pregnant or breastfeeding females. * Any concurrent severe or uncontrolled medical disease which places the subject at unacceptable risk if he/she were to participate in the study or confounds the ability to interpret data from the study. * Use of any other experimental drug or therapy within 28 days of first dose of amrubicin. * Known hypersensitivity to thalidomide or lenalidomide. * The development of erythema nodosum if characterized by a desquamating rash while taking thalidomide or similar drugs. * LVEF ≤ 50%. * Concurrent use of other anti-cancer agents or treatments. * Known positive for HIV, or infectious hepatitis, type B or C. * Cranial radiotherapy ≤ 21 days prior to first dose of amrubicin; radiotherapy to all other areas ≤ 7 days prior to first dose of amrubicin.