A Study of Ixazomib Plus Lenalidomide and Dexamethasone in Adult Japanese Participants With Relapsed and/or Refractory Multiple Myeloma

Inclusion Criteria: 1. Male or female Japanese participants 20 years of age or older. 2. Multiple myeloma (MM) diagnosed according to standard criteria either currently or at the time of initial diagnosis. The initial diagnosis must be symptomatic MM, although the relapsed disease does not need to be symptomatic. 3. Participants must have measurable disease defined by at least 1 of the following 3 measurements based on central laboratory data: * Serum M-protein: \>=1 g/dL (\>= 10 g/L). * Urine M-protein: \>=200 mg/24 hours. * Serum free light chain assay: involved free light chain level \>=10 mg/dL (\>= 100 mg/L), provided that the serum free light chain ratio is abnormal. 4. Participants with RRMM who have received 1 to 3 prior therapies. This participant population includes the following 3 categories of participants: * Participants who relapsed from their therapy(s) but were not refractory to any previous therapy. * Participants who were refractory to all lines of previous therapy(s) (ie, participants who have never responded to any therapies received). * Participants who were relapsed from at least 1 line of therapy AND additionally were refractory to at least 1 line of therapy. For the purposes of this study, refractory MM is defined as PD on therapy or PD within 60 days after the last dose of a given therapy. A line of therapy is defined as 1 or more cycles of a planned treatment program. This may consist of 1 or more planned cycles of single-agent therapy or combination therapy, as well as a sequence of treatments administered in a planned manner. For example, a planned treatment approach of induction therapy followed by autologous stem cell transplantation, followed by maintenance is considered 1 line of therapy. Autologous and allogenic transplants are permitted. 5. Participants must meet the following clinical laboratory criteria: * Absolute neutrophil count (ANC) \>= 1,000/mm3, hemoglobin \>= 8 g/dL and platelet count \>= 75,000/mm3. Platelet transfusions to help participants meet eligibility criteria are not allowed within 3 days prior to screening. * Total bilirubin =\< 1.5 x the upper limit of the normal range (ULN). * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 3 x ULN. * Calculated creatinine clearance \>= 30 mL/min. 6. Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2. 7. Participants who received prior allogenic transplant must have no active graft-versus-host disease (GVHD). 8. Participants who meet the following conditions: Female participants who: * Are postmenopausal for at least 24 months before the screening visit, OR * Are surgically sterile, OR * Females of childbearing potential must: 1. Have a negative pregnancy test with a sensitivity of at least 25 mIU/mL within 10 to 14 days and again within 24 hours prior to starting Cycle 1 of lenalidomide 2. Agree to practice true abstinence or to begin TWO reliable methods of birth control (1 highly effective method and 1 additional effective method AT THE SAME TIME) for at least 28 days before starting the study treatment through 90 days after the last dose of the study treatment. 3. Agree to ongoing pregnancy testing 4. Adhere to the guidelines of the RevMate program Male participants, even if surgically sterilized (ie, status postvasectomy), must: * Agree to avoid sexual intercourse completely 90 days after the last dose of the study treatment. * Agree to practice true abstinence or to practice effective barrier contraception during the entire study treatment period and 90 days after the last dose of the study treatment if their partner is of childbearing potential, even if they have had a successful vasectomy, and * Adhere to the guidelines of the RevMate program 9. Thromboembolism prophylaxis is required based on published standard or institutional standard of care. 10. Voluntary written consent must be given before performance of any study-related procedure not part of standard medical care, with the understanding that consent may be withdrawn by the participant at any time without prejudice to future medical care. 11. Participant is willing and able to adhere to the study visit schedule and other protocol requirements. Exclusion Criteria: 1. Participants who were refractory to lenalidomide or proteasome inhibitor-based therapy at any line. Refractory disease is defined as PD on treatment or PD within 60 days after the last dose of a given therapy. Participants who progressed the disease after 60 days from the last dose of a given therapy will be considered relapsed and are eligible for inclusion in the study. Participants who were refractory to thalidomide-based therapy are eligible. 2. Female participants who are breast feeding or pregnant. 3. Failure to have fully recovered (ie, =\< Grade 1 toxicity) from the effects of prior chemotherapy (except for hair loss) regardless of the interval since the last treatment. 4. Major surgery within 14 days before enrollment. 5. Radiotherapy within 14 days before enrollment. 6. Central nervous system involvement. 7. Infection requiring systemic antibiotic therapy or other serious infection within 14 days before enrollment. 8. Rash or pruritus requiring systemic medication within 14 days before enrollment. 9. Diagnosis of Waldenstrom's macroglobulinemia, polyneuropathy, organomegaly, endocrinopathy, monoclonal gammopathy, and skin changes (POEMS) syndrome, plasma cell leukemia, primary amyloidosis, myelodysplastic syndrome, or myeloproliferative syndrome. 10. Evidence of current uncontrolled cardiovascular conditions, including uncontrolled hypertension, uncontrolled cardiac arrhythmias, symptomatic congestive heart failure, unstable angina, or myocardial infarction within the past 6 months before enrollment. 11. Systemic treatment with strong cytochrome P450, family 3, subfamily A (CYP3A) inducers (rifampicin, carbamazepine, phenytoin), or St. John's wort within 14 days before enrollment. 12. Ongoing or active systemic infection, known human immunodeficiency virus (HIV)- positive, known hepatitis B surface antigen seropositive or known hepatitis C virus (HCV)-RNA positive. Participants who have positive hepatitis B core antibody (HBcAb) can be enrolled but must have hepatitis B virus (HBV)-DNA negative. Participants who have positive hepatitis C antibody can be enrolled but must have HCV-RNA negative. 13. Comorbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the participant inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens (eg, peripheral neuropathy that is Grade 1 with pain or Grade 2 or higher of any cause). 14. Psychiatric illness/social situation that would limit compliance with study requirements. 15. Known allergy to any of the study medications, their analogues, or excipients in the various formulations of any agent. 16. Inability to swallow oral medication, inability or unwillingness to comply with the drug administration requirements, or gastrointestinal condition that could interfere with the oral absorption or tolerance of treatment. 17. Diagnosed or treated for another malignancy within 2 years before enrollment or previously diagnosed with another malignancy and have any evidence of residual disease. Participants with nonmelanoma skin cancer or carcinoma in situ of any type are not excluded if they have undergone complete resection. 18. Participants who have participated in a clinical trial of ixazomib, or have been treated with ixazomib.