This study is conducted to determine the side effects related to LY2775240 given orally to healthy participants. Blood tests will be done to check how much LY2775240 is absorbed into the bloodstream and how long the body takes to get rid of it. Each participant will enroll in either Part A or Part B of the study, which will last about 14 weeks and 8 weeks respectively, including screening.

Inclusion Criteria:

• Overtly healthy adult male or a female who cannot get pregnant
• Have a screening body mass index (BMI) of greater than 18 and less than or equal to 32 kilograms per meter square (kg/m²), inclusive
• Have normal blood pressure, pulse rate, electrocardiogram (ECG) and medical test results that are acceptable for the study

Exclusion Criteria:

• Are currently participating in or completed a clinical trial within the last 30 days from a clinical trial or any other type of medical research judged to be incompatible with this study
• Have known allergies to compounds or drugs similar to LY2775240 or apremilast
• Have previously participated or withdrawn from this study
• Have or used to have health problems or medical test results or ECG readings that, in the opinion of the doctor, could make it unsafe to participate, or could interfere with understanding the results of the study