The main purpose of this study is to look at the amount of the study drug LY3938577 that gets into the blood stream and how long it takes the body to get rid of it. At a later stage of this study (part B and C) the blood sugar lowering effect and the duration of action of LY3938577 will be evaluated compared to Insulin Degludec. The study will also evaluate the safety and tolerability of LY3938577 and information about any side effects experienced will be collected. The study will be conducted in four parts (A, B, C, and D). Healthy participants in Part A Period 1 will receive a single dose of LY3938577 or a placebo given via intravenous (IV) infusion. In Part A Period 2, participants will receive a single subcutaneous (SC) dose of either LY3938577 or placebo. Participants in Part B with Type 1 Diabetes Mellitus (T1DM) will receive single doses of either LY3938577 or Insulin Degludec given via IV infusion. Participants in Part C with Type 1 Diabetes Mellitus (T1DM) will receive two doses of either LY3938577 or Insulin Degludec administered SC. Participants in Part D with Type 1 Diabetes Mellitus (T1DM) will be evaluated in 2 periods, with Period 1 administered pre-study basal insulin and lispro mealtime insulin to establish insulin needs, and Period 2 administered lispro mealtime insulin and daily doses of LY3938577. The study will last up to approximately 11 weeks for Part A, 10 weeks for Part B, 13 weeks for Part C, and 10 weeks for Part D , including screening period.