The main purpose of this study is to evaluate the safety and tolerability of LY3541105 in healthy and overweight participants. Blood tests will be performed to check how much LY3541105 gets into the bloodstream and how long it takes the body to eliminate it. The study will also evaluate the effects of LY3541105 on body weight and assess safety and tolerability of LY3541105. This is a 3-part study and may last up to 15, 26 and 24 weeks for each participant and may include up to 7, 15 and 16 visits in parts A, B and C, respectively.

Inclusion Criteria:

• Participants who are overtly healthy as determined by medical evaluation
• Male participants who agree to refrain from sperm donation and to use contraceptive methods and female participants not of childbearing potential
• Have a body mass index (BMI) in the range of greater than or equal to (>/=) 18.5 to less than (<) 32 kilogram per square meter (kg/m²), both inclusive (in Part A) or a BMI in the range of >/=27 to <40 kg/m², both inclusive (in Part B and C)
• Have had a stable weight for the last 3 months

Exclusion Criteria:

• Have history of diabetes (except gestational diabetes) or current diagnosis of diabetes
• Clinically significant abnormal electrocardiogram (ECG) at screening, as judged by the Investigator
• Have history or current evidence of a clinically significant cardiovascular condition