A Study to Evaluate the Effect of LY2189265 on the Speed at Which Food and Drink Leaves the Stomach in Patients With Type 2 Diabetes Mellitus

Inclusion Criteria: 1. Are males or females, diagnosed with Type 2 Diabetes Mellitus for greater than or equal to 3 months prior to screening. 2. Male patients agree to use a reliable method of birth control during the study and for 3 months following the last dose of study drug. Female patients must be of non-child-bearing potential due to surgical sterilization or menopause. 3. Have a body mass index (BMI) between 18.5 and 40.0 kilogram/square meter (kg/m²), inclusive. 4. Have Type 2 Diabetes Mellitus controlled with diet and exercise alone or are stable on a single oral antidiabetic medication (e.g. metformin) prior to screening, and have been taking a stable dose for \>7 days prior to the first dosing occasion. 5. Have a fasting blood glucose value at screening \>126 milligram/deciliter (mg/dL) (7.0 \[millimoles/liter\] mmol/L) for patients on a controlled diet, and \>108 mg/dL (6.0 mmol/L) for patients on oral antidiabetic medication, with an upper limit of 180 mg/dL (approximately 9.9 mmol/L) in each case. 6. Have a hemoglobin A1c (HbA1c) (indicates what your average blood glucose level has been in the past 3 months) value at screening (or within 4 weeks prior to screening) of 6.5% to 9.5%. If HbA1c is between 6.1% and 6.5%, patients may participate in the study providing they are receiving permissible oral antidiabetic medication. 7. Have clinical laboratory test results within normal ranges as determined by the study doctor. 8. Can provide enough blood in order to undergo the blood sampling required for the study. 9. Are reliable and willing to make themselves available for the duration of the study and are willing to follow study procedures. 10. Have signed the consent form approved by Lilly and the Ethical Review Board (ERB) governing the site. Exclusion Criteria: 11. Are currently enrolled in, or discontinued within the last 30 days from, a clinical trial involving an investigational drug or device, or are concurrently enrolled in any other type of medical research judged not to be scientifically or medically compatible with this study. 12. Have previously been exposed to, or have known allergies to glucagon-like-peptide-1 (GLP-1)-related compounds including LY2189265. 13. Are persons who have previously completed or withdrawn from this study or any other study investigating LY2189265 or have received glucagon-like peptides or incretin mimetics in the past 3 months. 14. Have taken certain Type 2 Diabetes medications within 30 days prior to screening. 15. Have an abnormality in the electrocardiogram (ECG) performed at screening. 16. Have poorly controlled high blood pressure (systolic blood pressure \>160 millimeters of mercury \[mmHg\] and/or diastolic blood pressure \>100 mmHg). 17. Have a history or presence of respiratory, liver, kidney, hormonal, blood, or neurological disorders which may put the patient at risk when taking the study medication; or may interfere with the interpretation of data. 18. Have a history or presence of cardiovascular disorder within the last year, or signs of congestive heart failure, or are expected to require coronary artery bypass surgery or angioplasty. 19. Have a history or presence of pancreatitis or certain gastrointestinal disorders. 20. Have been exposed to radiation from clinical trials and from diagnostic X-ray or are exposed routinely via your job worker. 21. Have any non-removable metal objects such as metal plates, screws etc. in their chest or abdominal area. 22. Have had acute diarrhea or constipation within 14 days of study screening. 23. Show evidence of significant active neuropsychiatric disease. 24. Regularly use known drugs of abuse and/or show positive findings on urinary drug screening. 25. Intend to start new medication during the study, including over-the-counter and herbal medication. 26. Have donated blood of more than 500 milliliter (mL) within the last month prior to screening. 27. Have an average weekly alcohol intake that exceeds the study centre's guidelines and are unwilling to adhere to the alcohol restrictions in place throughout the study. 28. Smoke more than 10 cigarettes (or equivalent in nicotine) per day, and are unwilling to stop smoking on the day of medication administration or are unable to abide by clinical research unit (CRU) restrictions on other inpatient days. 29. Are allergic to eggs or other components of the meals to be served. 30. Are patients who, in the opinion of the investigator, are in any way unsuitable to participate in the study.