The purpose of this study is to evaluate how well LY4057996 is tolerated and what side effects may occur in healthy participants and participants with Type 1 and Type 2 Diabetes. The study drug will be administered either subcutaneously (SC) (under the skin) or intravenously (IV) (into a vein in the arm). Blood tests will be performed to check how much LY4057996 gets into the bloodstream and how long it takes the body to eliminate it.

The study will last 11 weeks for Part A1-A2, 4 weeks for A3-A5, 6 weeks for Part B and 7 weeks for Part C, all approximations, excluding a screening period.

Inclusion Criteria:

Part A for Healthy Participants:

• Are overtly healthy as determined by medical evaluation, including medical history, physical exam, laboratory tests, and cardiac screening assessment

Part A for Type 2 Diabetes (T2DM) Participants:

• Are participants with T2DM diagnosed greater than 1 year before enrollment,
• On basal insulin therapy, insulin glargine, insulin detemir, or insulin degludec, greater than 10 units per day for at least 6 months (for Cohort 5 only)
• Glycated hemoglobin (HbA1c) 6.5% to 9.5% inclusive at screening

Part B

• Have Type 1 Diabetes (T1D) for at least 1 year with a fasting C-peptide level of 0.20 nanomole per liter (nmol/L) or less or non-fasting C-peptide level of 0.30 nmol/L or less at screening
• HbA1c 6% to 8.5% inclusive at screening

Part C

• Have T1D for at least 1 year with a fasting C-peptide level of 0.20 nanomole per liter (nmol/L) or less or non-fasting C-peptide level of 0.30 nmol/L or less at screening
• HbA1c 6 to 8.5% inclusive at screening

All Parts

• Have blood pressure of less than 140/90 millimeters of mercury (mmHg) for healthy participants or 150/90 mmHg for participants with diabetes and pulse rate of less than 90 beats per minute (bpm) (supine)
• No hypoglycemia unawareness for all Type 1 and Type 2 Diabetes participants

Exclusion Criteria:

• Have had more than 1 emergency room visit or hospitalization due to poor glucose control (hyperglycemia or diabetic ketoacidosis) within 6 months prior to screening
• Have had any episodes of severe hypoglycemia (defined as requiring assistance due to neurologically disabling hypoglycemia), hypoglycemia unawareness, or both within the 6 months prior to screening

All Parts

• Cardiovascular: no significant history of cardiovascular disease (CVD)
• Gastrointestinal: have gastroparesis or have undergone gastric surgery
• Hepatic: have acute or chronic hepatitis

Part A is Double-Blinded, Parts B and C are Open-Label