A Study of LY2409021 in Patients With Type 2 Diabetes

Inclusion Criteria: * Have a diagnosis of Type 2 diabetes mellitus according to the World Health Organization (WHO) diagnostic criteria * Are women not of child-bearing potential due to surgical sterilization (hysterectomy or bilateral oophorectomy or tubal ligation) or menopause. * Are male patients using a reliable method of birth control during the study and until 3 months after the last dose of study medication. * Are being treated with either diet and exercise alone, or with diet and exercise in combination with metformin. Metformin therapy must have been stable and unchanged for at least 3 months prior to screening and at a dose of at least 1000 milligram per day (mg/day). * Have a hemoglobin A1c (HbA1c) value of 7.0% to 10.5%, inclusive. * Have a body mass index (BMI) between 25 to 45 kilogram per meter squared (kg/m\^2), inclusive. In the opinion of the investigator, are capable and willing to: * Perform self-monitoring of blood glucose * Complete a study diary as required for this protocol * Maintain consistent dietary, physical activity, and sleeping patterns throughout the duration of the study * Comply with treatment regimens * Have given written informed consent to participate in this study in accordance with local regulations and the Ethical Review Board (ERB) governing the study site. Exclusion Criteria: * Have more than 1 episode of severe hypoglycemia (defined as an event during which the patient requires the assistance of another person to actively administer carbohydrate, glucagon, or other resuscitative actions) within 6 months prior to screening, or have a current diagnosis of hypoglycemia unawareness. * Have had two or more emergency room visits or hospitalizations due to poor glucose control in the 6 months prior to screening. * Have gastrointestinal disease that may significantly impact gastric emptying or motility or have undergone gastric bypass or gastric banding surgery. * Have had a previous diagnosis of pancreatitis. * Have New York Heart Association (NYHA) class II, III, or IV symptoms of heart failure * Have a history of myocardial infarction, unstable angina, or a coronary revascularization procedure within 6 months of screening. * Have a history of supraventricular tachycardia, ventricular tachycardia, or other cardiac arrhythmia. * Have a history of transient ischemic attack (TIA) or stroke within 6 months of screening. * Have poorly controlled hypertension (systolic blood pressure greater than or equal to 150 mm Hg or diastolic blood pressure greater than or equal to 90 mm Hg) as determined by the mean of three separate measurements. * Show evidence of labile blood pressure, including symptomatic postural hypotension. * Have any abnormality of the ECG that would impact patient safety or data interpretation. * Show clinical signs or symptoms of liver disease, or liver function tests (LFTs; aspartate aminotransferase \[AST\] or alanine aminotransferase \[ALT\]) greater than 2.5 times upper limit of normal (ULN) as determined by the central laboratory at screening. * Have a current or previous diagnosis of Gilbert's disease. * Have previous or current diagnosis of Hepatitis B or C * Have a serum creatinine \>2 milligrams per deciliter (mg/dL) or, in patients being treated with metformin, a serum creatinine above (or creatinine clearance below) what is approved in the metformin product labeling in the respective country. * Show evidence of uncorrected hypothyroidism or hyperthyroidism based on clinical evaluation and/or an abnormal thyroid stimulating hormone result as determined by the central laboratory at screening; patients receiving dose-stable thyroid replacement therapy for at least 3 months prior to screening will be allowed to participate in the study. * Have any other abnormal laboratory value that, in the opinion of the investigator, precludes the patient from participation in the study. Laboratory abnormalities consistent with type 2 diabetes mellitus and all other eligibility criteria are acceptable: for example, abnormalities of blood glucose, hemoglobin A1c (HbA1c), urinary glucose, and urinary protein (with a range of trace to 1+ on dipstick). * Have a currently suspected or treated malignancy, or are in remission from a clinically significant malignancy (other than basal or squamous cell skin cancer, in situ carcinomas of the cervix, or in situ prostate cancer) for less than 5 years. * Have a personal or family history of pancreatic neoplasia. * Have non-fasting triglycerides \>600 mg/dL. * Use or have used insulin or GLP-1 agonists (for more than 1 week within the 3-month period prior to screening), or any oral antihyperglycemic medication (OAM) other than metformin within the 3-month period prior to screening. * Currently use or intend to use prescription or over-the-counter medications, including herbal supplements, to promote weight loss or to regulate blood glucose. * Have current chronic (\>2 weeks) systemic glucocorticoid therapy (excluding ocular topical, other topical, inhaled preparations) or have received such therapy within 8 weeks prior to screening. * Currently use hyperglycemia-causing agents, hypoglycemia-causing agents (other than metformin), class II and III antiarrythmic agents, agents that reduce gastrointestinal motility, central nervous system stimulants (with the exception of caffeinated beverages), fibrates, and niacin greater than or equal to 1 grams per day (gm/day). * Have an average weekly alcohol intake that exceeds 2 units per day for males and 1 unit per day for females (1 unit = 12 ounces (oz) or 360 mL of beer; 5 oz or 150 milliliters (mL) of wine; 1.5 oz or 45 milliliter (mL) of distilled spirits). * Currently use drugs with a narrow therapeutic index (for example, digoxin, lithium, phenytoin, theophylline, and warfarin). * Currently use drugs that are known to prolong the QT interval. * Currently use or intend to use potent inhibitors of CYP3A, which include but are not limited to atazanavir, indinavir, nelfinavir, ritonavir, clarithromycin, itraconazole, ketoconazole, nefazodone, saquinavir, and telithromycin. * Have previously completed or withdrawn from this study or any other study investigating LY2409021. * Have known allergies to LY2409021 or related compounds. * Are currently enrolled in, or discontinued within the last 30 days from, a clinical trial involving an investigational product or unapproved use of a drug or device, or concurrently enrolled in any other type of medical research judged not to be scientifically or medically compatible with this study * Have any other condition such as alcohol abuse, drug abuse, or psychiatric disorder that may affect the ability to participate in the trial.