The main purpose of this study is to assess the safety and tolerability of a single dose of LY3938577 in healthy participants and participants with Type 2 Diabetes Mellitus (T2DM) (Part A) and multiple doses of LY3938577 in participants with T2DM (Part B). The study will last approximately 6 weeks for Part A and approximately 10 weeks for Part B respectively.

Inclusion Criteria:

• Male and female participants who are overtly healthy as determined by medical evaluation (Part A)
• Participants with T2DM diagnosed greater than 1 year before enrollment (Part A and Part B)
• Have a body mass index within the range of 18.5 to less than or equal to (<=) 32 kilograms per square meter (kg/m²) for healthy participants and 18.5 to 40 kg/m² for T2DM participants.
• Male or female participants of nonchildbearing potential

Exclusion Criteria:

• Have proliferative retinopathy or maculopathy and/or severe neuropathy
• Have been treated with sulfonylurea, thiazolidinedione, alpha-glucosidase inhibitor, glucagon-like peptide-1 receptor agonist or Insulin within the previous 3 months
• Have received chronic systemic glucocorticoid therapy in the past 3 months
• Are currently enrolled in another clinical study trial involving medical research, or have participated within the last 30 days in a clinical study involving an investigational product.