The purpose of this study is to measure how much LY3537031 gets into the bloodstream and how long it takes the body to eliminate it in participants with mild, moderate and severe impaired liver function and in healthy participants with normal liver function. The safety and tolerability of LY3537031 will also be evaluated. The study drug will be administered subcutaneously (SC) (under the skin).

Inclusion Criteria:

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

Additional Inclusion Criteria for Participants Without Hepatic Impairment in Group 1:

• Are healthy participants as determined by medical history, physical examination, and other screening procedures, with clinically normal hepatic function at screening
• Have normal blood pressure (BP) and pulse rate, as determined by the investigator

Additional Inclusion Criteria for Participants with Mild to Severe Hepatic Impairment in Groups 2 through 4:

• Participants with hepatic impairment classified as Child-Pugh score A, B, or C who are considered acceptable for participation in this study by the investigator. Participants must have a diagnosis of chronic hepatic impairment of greater than 6 months per physician diagnosis and standard-of-care practice, with no clinically significant changes, in the opinion of the investigator, within 15 days prior to screening
• Clinical laboratory test results with deviations that are judged by the investigator to be compatible with the hepatic impairment of the participant, or of no additional clinical significance for this study. Abnormalities of serum glucose, serum lipids and triglycerides, urinary glucose, and urinary protein consistent with Type 2 Diabetes Mellitus (T2DM) are acceptable
• Have a systolic BP less than 150 millimeters mercury (mmHg), a diastolic BP less than 90 mmHg, and a pulse rate greater than 50 but less than 100 beats per minute
• If participants have T2DM, they must have a hemoglobin A1c measurement equal to or less than 11.5% at the screening visit

Exclusion Criteria:

• Have significant history of or current cardiovascular, respiratory, hepatic (hepatic applies to Group 1 only), renal, gastrointestinal (GI), endocrine, hematological, dermatological, or neurological disorders capable of significantly altering the absorption, metabolism, or elimination of drugs; of constituting a risk when taking the investigational medicinal product; or of interfering with the interpretation of data
• Have a history of atopy; that is, severe or multiple allergic manifestations, or clinically significant multiple or severe drug allergies, or hyperesthesia, or severe posttreatment hypersensitivity reactions, or have known allergies to LY3537031, or related compounds
• Have undergone any form of bariatric surgery
• Have a history of or current acute or chronic pancreatitis, or elevation in serum lipase or amylase or both greater than 1.5× upper limits of normal (ULN)