A Study of the Safety and Effectiveness of LY3053102 in Participants With Type 2 Diabetes

Inclusion Criteria * Participants with type 2 diabetes mellitus for at least 6 months before entering the trial based on the disease diagnostic criteria (World Health Organization \[WHO\]) classification managed with diet or exercise alone or with a stable dose of metformin of at least 1000 mg/day for at least 60 days before screening or on metformin and an eligible second oral anti-hyperglycemic medication after a 60-day washout of the second oral anti-hyperglycemic medication * Women not of childbearing potential due to surgical sterilization (hysterectomy or bilateral oophorectomy or tubal ligation) or menopause * Have a hemoglobin A1c value of ≥7.0% and ≤10.5%, if on diet and exercise or diet, exercise, and metformin (stable dose of at least 1000 mg/day for at least 60 days), or have a hemoglobin A1c value of ≥7.0% and ≤9.5%, and are on an appropriate diet and exercise regimen, a stable dose of metformin and willing to discontinue a second oral anti-hyperglycemic medication * Have a body mass index ≥23 and ≤45 kilograms per square meter (kg/m\^2) Exclusion Criteria * Have used insulin for diabetic control for more than 6 consecutive days within 1 year prior to screening * Have used thiazolidinediones within 3 months, or any other drugs for treatment of hyperglycemia (except metformin) within 2 months, prior to the first week of the study * Have hepatitis B and/or positive hepatitis B surface antigen. hepatitis C or human immunodeficiency virus (HIV) and/or positive HIV antibodies * Have known or suspected cardiac autonomic neuropathy (for example, resting tachycardia or orthostatic hypotension), based on clinical signs, symptoms, or appropriate diagnostic testing * Have cardiac disease with functional status that is New York Heart Association Class II, III, or IV or in the last 6 months have had any of the following: a history of myocardial infarction , unstable angina, coronary artery bypass graft, percutaneous coronary intervention (diagnostic angiograms are permitted), transient ischemic attack, or cerebrovascular accident (for example, stroke) * Have poorly controlled hypertension, malignant hypertension, renal artery stenosis, and/or evidence of labile blood pressure including symptomatic postural hypotension. Doses of antihypertensive medications must be stable for 30 days prior to the first week of the study * Have obvious clinical signs or symptoms of liver disease, acute or chronic hepatitis, or an alanine transaminase or aspartate aminotransferase levels \>2 times the upper limit of the reference range * Have evidence of hypothyroidism or hyperthyroidism based on clinical evaluation and/or an abnormal thyroid-stimulating hormone which, in the opinion of the investigator, would pose a risk to participant safety. Participants on a stable dose of thyroid replacement therapy may be eligible if they meet the other criteria * Have clinically significant peripheral vascular disease, or clinical evidence of active diabetic proliferative retinopathy, (known significant autonomic neuropathy) as evidenced by urinary retention, orthostatic hypotension, diabetic diarrhea or gastroparesis * Have an active or untreated malignancy or have been 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 impaired renal function * Have fasting triglycerides \>500 milligrams per deciliter (mg/dL) at screening * Have experienced a keto-acidotic episode requiring hospitalization in the last 6 months * Have an electrocardiogram (ECG) considered to be indicative of cardiac disease * Have personal or family history of long QT syndrome, family history of sudden death in a first-degree relative before age 40, or personal history of unexplained syncope within the last year. Use of prescription or over-the-counter medications known to prolong the QT or QTc interval * Have a history of bone disease (including osteoporosis or unhealed fractures), evidence of osteoporosis (femoral neck or lumbar spine T-score \<-2.5) determined by dual X-ray absorptometry (DXA) scan at screening, evidence of osteopenia (T-score between -1.0 and -2.5 at the femoral neck or lumbar spine) with a high risk of fracture based on risk factors or current active treatment of periodontal disease