The main purpose of this study is to evaluate how the body absorbs and removes LY2605541, insulin lispro, and a mixture of both from the blood. The study has two parts. Participants may enroll in only one part. Each part has four treatment periods in a fixed order. The study will last approximately 8 weeks, not including screening. Screening is required within 28 days prior to the start of the study.

Inclusion Criteria:

• Are not of child-bearing potential
• Have a body mass index (BMI) between 18 and 29.9 kilograms per meter squared (kg/m^2), inclusive
• Are nonsmokers or have not smoked for at least 2 months prior to entering the study

Exclusion Criteria:

• Have known allergies to insulin or its excipients, or related drugs, or history of relevant allergic reactions of any origin
• Have a history of first-degree relatives known to have diabetes mellitus
• Have used systemic glucocorticoids within 3 months prior to entry into the study
• Have donated blood or had a blood loss of 450 milliliter (mL) within 1 month prior to study enrollment