A First-in-Human Study of LY2409021 in Healthy Participants and Participants With Type 2 Diabetes

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