Safety, Tolerability and Pharmacokinetics of Multiple Rising Doses of Ixazomib in Lupus Nephritis (LN)

Inclusion Criteria: 1. In the opinion of the investigator, is capable of understanding and complying with protocol requirements. 2. The participant or, when applicable, the participant's legally acceptable representative signs and dates a written informed consent form and any required privacy authorization prior to the initiation of any study procedures. 3. Is female or male and aged 18 to 75 years, inclusive. 4. Has a diagnosis of systemic lupus erythematosus (SLE) defined by meeting either the 2012 Systemic Lupus International Collaborating Clinics (SLICC) criteria or the American College of Rheumatology (ACR) criteria for the classification of SLE. The 4 criteria required by ACR classification are not required to be present at Screening for eligibility. 5. Has a definite diagnosis of LN based on a kidney biopsy done within 2 year of the Screening Visit which demonstrated International Society of Nephrology/Renal Pathology Society (ISN/RPS) class III, IV or V changes \[excluding Class III (C), IV-S (C) and IV-G (C)\] or World Health Organization (WHO) 1982 classification Class III,IV or V(excluding Class IIIc and IVd). 1. If no biopsy was done within 2 year of Screening Visit, biopsy can be done during the screening period as a study procedure. 2. Co-existence of classes is permitted. 6. Has a renal biopsy demonstrating either ISN/RPS or WHO class V or class V with class 2 nephritis with a UPCR of greater than (\>) 3 or the participant has a renal biopsy demonstrating either active ISN/RPS or WHO class III or IV nephritis, defined by either one of the following criteria: a) A UPCR\* of \>=1.0 at Screening OR b) A UPCR\* \>0.5 at Screening and at least one of the following: i. Active urine sediment in the absence of infection or other cause within 3 months of screening, defined as at least one of the following: * \>=5 red blood cells (RBC) per high power field, not due to causes other than lupus nephritis. * \>=5 white blood cells (WBC) per high power field in the absence of infection. * Presence of cellular casts. ii. The participant has increased levels (above upper limit of normal \[ULN\]) serum dsDNA autoantibodies at screening. iii. Low complement (either C3 or C4) at Screening (\>= 25 percent \[%\] lower than lower limit of normal \[LLN\]). iv. Biopsy within 3 months prior to screening visit indicating active proliferative lupus glomerulonephritis ISN/RPS class III or IV changes \[excluding Class III (C), IV-S (C) and IV-G (C)\] or WHO 1982 classification Class III or IV (excluding Class IIIc and IVd), with co-existing Class V permitted. * Participants may be re-screened once for urinary sediment, proteinuria or complement levels within 2 weeks of the original screening visit. * UPCR value for eligibility will be based on the average UPCR obtained from the 3 specimens collected during screening. 7. Has had an inadequate response, in the judgment of the Investigator, to at least 6 months of an immunosuppressive regimen including single or sequential use of at least one of the following: cyclophosphamide (CYC), mycophenolate mofetil (MMF), mycophenolic acid (MA), or azathioprine (AZA). 8. If the participant is on glucocorticosteroids, must be on stable dose equivalent to 20 mg/day or less of prednisone for at least 2 weeks prior to first dose of study medication. Participant who are on a stable dose equivalent to \>20 mg/day and \<=30 milligram per day (mg/day) of prednisone may be allowed to the study if reviewed by the adjudication committee and approved by the medical monitor; however, the steroid dose should be tapered. 9. Male participants who are sexually active with women of child bearing potential (WOCBP), even if surgically sterilized (that is, status post-vasectomy), must: a) Agree to practice effective barrier contraception during the entire study treatment period and through 90 days after the last dose of study drug. 10. Female participants who are of child bearing potential must: a) Agree to practice 2 effective methods of contraception, at the same time, from the time of signing the informed consent through 90 days after the last dose of study drug. 11. This study permits the re-enrollment of a participant that has discontinued the study as a pre- treatment failure (ie, participant has not been randomized). If re-enrolled, the participant must be re-consented. \* The re-enrollment of all participants who completed Cohort A and B is permitted to subsequent cohorts (2.0 mg and 3.0 mg dose cohorts) after completion of all cycles including the follow-up period if they had no drug-related adverse events greater than Grade 1, no adverse events greater than Grade 2, continue to meet all inclusion and exclusion criteria, and the Safety Review Committee has reviewed and approved enrollment of the subject into a higher dose cohort. 12. Must be receiving Standard of Care (SOC) treatment with an immunosuppressant drug for the treatment of LN (example, MMF, MA or AZA). Exclusion Criteria: 1. Has received any investigational compound within 30 days or 5 half-lives, whichever is the longer, prior to Screening or is currently participating in another interventional clinical study. 2. Has received ixazomib, bortezomib, or another proteasome inhibitor in a previous clinical study or as a therapeutic agent. 3. Is a sponsor employee, an immediate family member, study site employee, or is in a dependent relationship with a study site employee who is involved in conduct of this study (example, spouse, parent, child, sibling), or may consent under duress. 4. Has an autoimmune disease other than SLE as their main diagnosis. 5. Has drug-induced SLE. 6. Has severe, active central nervous system (CNS) lupus (British Isles Lupus Assessment Group \[BILAG\] A or B). 7. Has an estimated eGFR of \<30 milliliter per minute per 1.73 m\^2 (mL/min/1.73m\^2), or is on dialysis, or is expected to have a renal transplant within 1 year of randomization, or has had a renal transplant. 8. Has a severe acute infectious disease (example, untreated active tuberculosis (TB), acute viral hepatitis, human immunodeficiency virus (HIV), untreated latent TB, or infections requiring IV anti-microbial treatment within 2 months preceding the Screening Visit. 9. Has a history of a malignant disease (except successfully treated basal cell carcinoma, squamous cell carcinoma, or cervical carcinoma in situ) within 5 years prior to Screening. 10. Has one of the following laboratory test values: 1. IgG\<75% of LLN 2. Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) \>3 times the central laboratory's ULN 3. Bilirubin \>1.5 x ULN (participants with Gilbert Syndrome with a confirmed diagnosis and documented in the subject's medical record will not be excluded based on this criterion). 4. Platelets \<75,000 per cubic millimeter (/mm\^3) 5. Neutrophils \<1500/ mm\^3 or \> 11,000/ mm\^3 6. Hemoglobin \<8 grams per deciliter (g/dL) 7. Positive for Hepatitis B Surface Antigen. 8. Positive for Hepatitis C antibody. 11. Has a history of drug or alcohol abuse or dependence (as defined by Diagnostic and Statistical Manual of Mental Disorders, fourth Edition \[DSM-IV\]) within 1 year prior to the screening visit. 12. If female, the participant is pregnant or lactating or intending to become pregnant before, during, or within 3 months after participating in this study; or intending to donate ova during such time period. 13. If male, the participant intends to donate sperm during the course of this study or for 90 days after the last dose. Male participants planning to father during clinical trial conduct or within 90 days after the last planned dose of trial treatment. 14. Has moderate or severe liver disease (Child-Pugh B or C), and/or positive serological tests for hepatitis B (other than due to prior immunization) or hepatitis C. 15. Is taking excluded medications. 16. Has a history of clinically significant neuropathies of National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) v 4.03 Grade 2 or higher. 17. Has been treated with CYC within 4 weeks of the Screening Visit. 18. Has been treated with \> 3 g/day of MMF within 4 weeks of the Screening Visit. 19. Has been treated with belimumab, abatacept or tocilizumab within 3 months of the Screening Visit. 20. Has been treated with eprazutumab, alemtuzumab, rituximab or other cell depleting biological agents within 6 months of the Screening Visit. 21. Current symptoms of severe, progressive, or uncontrolled non-SLE related renal, hepatic, hematological, gastrointestinal (including hypomotility and ulcerative/inflammatory conditions), pulmonary, cardiac, neurological, or cerebral disease, or other concomitant medical conditions that, in the opinion of the Investigator, might place the subject at unacceptable risk for participation in this study.