A Study of LY3938577 in Healthy Participants and Participants With Type 1 Diabetes Mellitus (T1DM)

Inclusion Criteria: Part A - • Participants who are overtly healthy as determined by medical history and physical examination. Parts B and C - * Have Type 1 Diabetes Mellitus (T1DM) for at least 2 years with a fasting C-peptide level of 0.20 Nanomoles Per Liter (nmol/L) or less, or nonfasting C-peptide level of 0.30 nmol/L or less at screening. * Have well-controlled HbA1c between 6.0% to 8.5 percent (%). * Insulin pump users with a total daily basal dose between 15 to 45 International Unit (IU). Part D - * Have T1DM for at least 1 year with a fasting C-peptide level of 0.20 nmol/L or less, or non-fasting C-peptide level of 0.30 nmol/L or less. * HbA1c between 6% to 8.5% inclusive. * Insulin pump users with a total daily basal dose between 15 to 45 International Unit (IU). * Insulin multiple daily injection users (glargine or degludec insulin) with a total daily insulin dose between 0.3 to \<1.2 (I)U/kg/day. * No hypoglycaemia unawareness. * Basal insulin dose that is between 30% to 70% of the total daily insulin dose * Are able to complete the exercise challenge test. All Parts - * Have normal blood pressure, pulse rate and safety laboratory test results that are acceptable for the study. * Have body mass index (BMI) between 18.0 and 35.0 kilograms per meter squared (kg/m²), inclusive, at screening. * Have venous access sufficient to allow for blood sampling. * Male and/or female not of childbearing potential. Exclusion Criteria: Parts B, C, and D - * Have had more than 1 emergency room visit or hospitalization due to poor glucose control (hyperglycemia or diabetic ketoacidosis) within the last 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 last 6 months prior to screening. Parts B and C - * Have been treated with Glucagon-like Peptide-1 Receptor Agonists (GLP-1 RA), Dipeptidyl Peptidase 4 (DPP4) inhibitor, Glucose-dependent Insulinotropic Polypeptide (GIP) agonists, Metformin, or Sodium-Glucose Transport Protein 2 (SGLT2) inhibitors within the previous 3 months. * Have received systemic or inhaled glucocorticoid therapy (excluding topical, intraarticular, and intraocular preparations) for more than 14 consecutive days within 4 weeks before screening. Part D - • Have been treated with Dipeptidyl peptidase-4 (DPP-IV) inhibitors, GLP-1 RA, GIP/GLP-1 RA, Metformin, Pramlintide, SGLT2 inhibitors, or Neutral Protamine Hagedorn (NPH) insulin within the previous 3 months. All Parts - * Have had any of the following cardiovascular conditions: acute myocardial infarction, New York Heart Association Class III or IV heart failure, or cerebrovascular accident (stroke). * Have gastroparesis or have undergone gastric bypass (bariatric) surgery or restrictive bariatric surgery (for example, Lap-Band®) prior to screening. * Have history of renal transplantation, currently receiving renal dialysis, have serum creatinine level of more than 2.00 milligrams per decilitre (mg/dL) or have an estimated glomerular filtration rate of less than 60.0 milliliters (mL) / minute /1.73 square meters. * Have acute or chronic hepatitis, or obvious clinical signs or symptoms of any other liver disease except non-alcoholic fatty liver disease (that is, participants with non-alcoholic fatty liver disease are eligible for participation), and/or have elevated liver enzyme measurements, as determined by the local laboratory at screening and as indicated: * Total bilirubin (TBL) \>2 × the Upper Limit of Normal (ULN) in the absence of Gilbert's syndrome, or * Alanine aminotransferase (ALT) /serum glutamic pyruvic transaminase (SGPT) \>2.5 × ULN, or * Aspartate aminotransferase (AST) /serum glutamic oxaloacetic transaminase (SGOT) \>2.5 × ULN.