The main purpose of this study is to evaluate the safety and tolerability of the study drug known as LY3108743 in healthy participants and in participants with type 2 diabetes.

The study will also investigate how LY3108743 affects the levels of blood sugar and other naturally occurring substances (e.g. hormones that control the way sugar is used) in the body, how much of the study drug gets into the blood stream, and how long it takes the body to get rid of it.

Information about any side effects that may occur will be collected. The study is expected to last approximately 7 to 8 weeks for each participant.

The study will have up to 3 parts. Participants may enroll in only one part.

Inclusion Criteria:

• Must be a male, or a female who cannot become pregnant, and who is either a healthy participant, or who has type 2 diabetes
• Have a body mass index (BMI) of 18.5 to 40.0 kilogram per square meter (kg/m^2), inclusive, at screening
• Have normal blood pressure
• Participants with diabetes must not be taking any anti-hyperglycemic medications with the exception of metformin. If on metformin, participants must be on a stable treatment regimen for at least for 4 weeks prior to screening
• Participants with diabetes must have a hemoglobin A1c (HbA1c) level between 6 to 11%, inclusive, at screening

Exclusion Criteria:

• Have previously completed or withdrawn from this study
• Have or used to have health problems or laboratory test results or electrocardiogram (ECG) readings that, in the opinion of the doctor, could make it unsafe to participate or could interfere with understanding the results of the study