The purpose of this study is to assess the amount of LY3537031 that reaches the bloodstream and the time it takes for the body to get rid of it when given to participants with renal (kidney) impairment and to healthy participants.

Inclusion Criteria:

• Have a body weight of 55 kilogram (kg) or more and body mass index (BMI) within the range 19.0 to 40.0 kilogram per square meter (kg/m²), inclusive
• Have no significant history of spontaneous or ethanol-induced hypoglycemia

Additional Inclusion Criteria for Healthy Participants in Control Group:

• Are healthy as determined by medical history, physical examination, and other screening procedures, with normal renal function, assessed by estimated glomerular filtration rate (eGFR) of at least 90 milliliter per minute (mL/min) at screening
• Have glycated hemoglobin (HbA1c) less than or equal to 6.5% at screening

Additional Inclusion Criteria for Participants with Severe Renal Impairment or with End-Stage Renal Disease (ESRD):

• Have stable severe renal impairment, assessed by eGFR less than 30 mL/min at screening, who have been on stable hemodialysis schedule for at least 3 months prior to planned dosing
• Have acceptable blood pressure and pulse rate
• If participants have Type 2 Diabetes Mellitus (T2DM), they must have a HbA1c equal to or less than 11.5% at the screening visit

Exclusion Criteria:

• Have a history of chronic liver disease, acute or chronic hepatitis, including a history of autoimmune hepatitis, any evidence for hepatic impairments
• Have a current, functional renal transplant. Non-functional renal allografts may be allowed
• Have a diagnosis or history of malignant disease within 5 years before screening (some exceptions are allowed)
• Have a family or personal history of medullary thyroid carcinoma or multiple endocrine neoplasia syndrome Type 2