The main purpose of this study is to learn more about the safety of LY3361237 and any side effects that might be associated with it when given to participants with systemic lupus erythematosis (SLE). LY3361237 will be administered by injections just under the skin. The study will last up to 26 weeks and may include up to 17 visits to the study center.

Inclusion Criteria:

• Participants must have received a diagnosis of SLE at least 24 weeks before screening (at least 4 of 11 criteria in 1997 revised American College of Rheumatology [ACR] classification)

• If a participant is taking oral prednisone (or prednisone equivalent) for SLE, the dose must be ≤20 milligrams per day (mg/day) for at least 8 weeks prior to screening, and must have been stable for at least the last 2 weeks

• If a participant is taking any of the following medications for SLE, the medication must have been used for at least 12 weeks and stable for at least the last 8 weeks:

  • Azathioprine ≤200 mg/day
  • Antimalarial (e.g., chloroquine, hydroxychloroquine, quinacrine)
  • Mycophenolate mofetil ≤2 g/day or mycophenolic acid ≤1.44 grams per day (g/day)
  • Oral, SC, or intramuscular methotrexate ≤15 milligrams per week (mg/week)

Exclusion Criteria:

• Participants must not have a history of, or current, inflammatory joint or skin disease other than SLE
• Participants must not have a current active bacterial, viral, or fungal infection
• Participants must not have evidence of significant liver or kidney dysfunction
• Participants must not have received cytotoxic medications (e.g., cyclophosphamide) within the last 3 months.
• Participants must not have received any intra-articular, intramuscular, or intravenous glucocorticoids within the last 3 months
• Participants must not have received blood products (e.g., blood transfusion, platelets, etc.) within the last 12 months