The main purpose of this study is to measure how much of LY3502970 gets into the bloodstream and how long it takes the body to eliminate it in participants with mild, moderate and severe impaired liver function compared to participants with normal liver function. The safety and tolerability of LY3502970 will also be evaluated. The study may last up to 6 weeks for each participant including the screening period.

Inclusion Criteria:

• Men or women with body weight of at least 45 kilograms and a body mass index of 18.5 to 40.0 kilograms per meter squared (kg/m²).
• Both healthy individuals and individuals with hepatic impairment classified as Child-Pugh Score A, B, C that is mild, moderate, or severe impairment, respectively, liver disease can participate who are considered acceptable for participation in this study by the investigator.
• Participants must have a diagnosis of chronic hepatic impairment for more than 6 months per physician diagnosis and standard of care practice, with no clinically significant changes within 15 days prior to study intervention administration.
• Participants may have mild stable baseline medical conditions for which neither the condition nor treatments received would negatively impact the health of the participant or study conduct.
• Have acceptable BP and pulse rate, as determined by the investigator at screening.
• No significant history of spontaneous or ethanol induced hypoglycemia.
• Participants with Mild to Severe Hepatic Impairment who have a hemoglobin level of at least 8.5 grams/deciliter.
• Participants with both T2DM and Hepatic Impairment have T2DM controlled with diet or exercise alone or on stable doses of anti-diabetic medications metformin or sulfonylureas, for at least 8 weeks prior to screening.
• Participants with both T2DM and Hepatic Impairment have a hemoglobin A1c greater than or equal to 5.0% and less than or equal to 11.0% at the screening visit.
• Participants with both T2DM and Hepatic Impairment have clinical laboratory test results within normal range or deemed clinically insignificant by the investigator. Abnormalities of serum glucose, serum lipids, urinary glucose, and urinary protein consistent with T2DM are acceptable.

Exclusion Criteria:

• Have significant history of, or current, cardiovascular, respiratory, hepatic (applies to Group 1 only), renal, GI, endocrine, hematological, or neurological disorders capable of significantly altering the absorption, metabolism, or elimination of drugs.
• Have a history or presence of pancreatitis, elevation in serum amylase or lipase (greater than 1.5-fold ULN) or GI disorder or any GI disease, which impacts gastric emptying.
• Have any abnormality in the 12-lead ECG at screening.
• Have severe atopy or have a history of clinically significant multiple or severe drug allergies or severe post treatment hypersensitivity reactions.
• Have a history of, or current psychiatric disorders.
• Women who are pregnant, intend to become pregnant or are breastfeeding a child are not eligible to participate.
• Have taken any glucose-lowering medications other than metformin, sulfonylureas, and insulin, in the past 6 weeks or 5 half-lives (whichever is longer) prior to planned dosing.

All enrolled participants.

Baseline up to end of follow-up (up to 14 days)

Safety population consisted of all enrolled participants who received at least one dose of LY3502970.