The main purpose of this study is to learn more about the safety of LY3537021 and any side effects that might be associated with it in healthy participants and participants with type 2 diabetes mellitus (T2DM). Blood tests will be performed to check how much LY3537021 gets into the bloodstream and how long the body takes to eliminate it.

This study will last up to about 19 weeks including screening period.

Inclusion Criteria:

• Are overtly healthy males or females not of childbearing potential, as determined through medical history and physical examination
• Contraceptive use by men should also be consistent with local regulations regarding the methods of contraception for those participating in clinical studies.
• Have a body mass index of 18.5 to 40 kilograms per square meter (kg/m²), inclusive
• Have hemoglobin A1c level of less than or equal to (≤)6.5 percent (%)

Patients with Type 2 Diabetes Mellitus (T2DM):

• Have T2DM for at least 6 months
• For Part A, have a hemoglobin A1c value at screening of 6.5% to 11% and are treated with diet and exercise alone or a stable dose of metformin for at least 3 months prior to screening. For Part B, have hemoglobin A1c value at screening of 6.5% to 10% and are treated with diet and exercise alone or a stable dose of metformin for at least 3 months prior to screening with or without 1 other OAM, such as DPP-IV inhibitors, SGLT-2 inhibitors, or sulfonylureas

Exclusion Criteria:

• Have an abnormality in the 12-lead electrocardiogram (ECG) that, in the opinion of the investigator, increases the risks associated with participating in the study or may confound ECG data analysis
• Have a history of malignancy within 5 years prior to screening
• Have obvious clinical signs or symptoms of liver disease, acute or chronic hepatitis
• Have evidence of significant active psychiatric disorder(s) as determined by the investigator
• Have undergone any form of bariatric surgery
• Have donated blood of 450 milliliters (mL) or more in the past 3 months or any blood donation within the past month from screening
• Have an average weekly alcohol intake that exceeds 21 units per week (males up to age 65 years) and 14 units per week (females and males above 65 years), or are unwilling to stop alcohol consumption 24 hours prior to dosing until discharge from the investigative site
• Smoke >10 cigarettes per day or the equivalent or are unable or unwilling to refrain from nicotine during investigative site admission

Patients with T2DM:

• Have had any of the following within the past 6 months prior to screening: myocardial infarction, unstable angina, coronary artery bypass graft, percutaneous coronary intervention (diagnostic angiograms are permitted), transient ischemic attack, cerebrovascular accident or decompensated congestive heart failure, or currently have New York Health Association Class III or IV heart failure
• Are currently treated with or within the past 3 months had treatment with GLP-1 receptor agonists, or insulin
• Have had severe hypoglycemic event in the last 3 months