The main purpose of this study is to determine the safety of LY2409021 in healthy participants and participants with diabetes. The study drug is given as single oral doses. Each participant can receive up to 3 doses, with a minimum 7 day washout between dosing periods. Side effects will be documented. This study is approximately 9 weeks long, not including screening. Screening is required within 6 weeks prior to the start of the study.

Inclusion Criteria:

For all participants:

• Must be either a male, or a female who cannot become pregnant, who is either healthy or have type 2 diabetes mellitus (T2DM) but not taking medication for diabetes
• Have an hemoglobin A1c (HbA1c) value of less than or equal to 10% at screening
• Have blood and urine laboratory test results that are acceptable for the study

For healthy participants:

• Have a screening body mass index (BMI) of 18.5 to 29.9 kg/m^2 inclusive
• Have a fasting blood glucose between 3.0-5.2 millimoles/liter (mmol/L) at screening
• Have plasma glucose, two hours after ingesting an oral 75 g glucose load, less than 7.8 mmol/L

For participants with type 2 diabetes mellitus (T2DM):

• Have a screening body mass index (BMI) of 18.5 to 35 kg/m^2 inclusive
• Must weigh 45 kg or more at screening
• Have a fasting blood glucose less than 11.1 mmol/L at screening
• Have plasma glucose, two hours after ingesting an oral 75 g glucose load, greater than or equal to 11.1 mmol/L

Exclusion Criteria:

For all participants:

• Have participated in a study with a new drug in the last 30 days
• Have a history of significant heart, lung, liver, kidney, stomach or brain disease, or have any medical problems which may cause an increased risk during the study
• Have hypertension requiring more than single-agent therapy, or blood pressure greater than 140/90 millimeters of mercury (mmHg) on monotherapy
• Are allergic to LY2409021 or similar drugs
• Have a regular alcohol intake greater than 21 units/week (male), or 14 units/week (female), or are unwilling to stop alcohol as required by the study restrictions (1 unit = 360 mL of beer, or 150 mL of wine, or 45 mL of spirits)
• Intend to use other over-the-counter or prescribed medicines during 7 or 14 days respectively before the study, or during the study. Medicines for high cholesterol and high blood pressure are allowed if you have diabetes.
• Have a significant blood disorder and/or donated blood (450 ml or more) in the last 3 months

For participants with T2DM:

• Have signs of having serious problems with diabetes (For example, severe eye problems, poorly healing skin)
• Have a history of being in a coma due to low blood sugar