A Study to Compare a New Long-Acting Insulin (LY2605541) and Human Insulin NPH in Participants With Type 2 Diabetes (IMAGINE 6)

Inclusion Criteria:

• Have had type 2 diabetes mellitus for at least 1 year, not treated with insulin
• Have been receiving 2 or more OAMS for at least 3 months prior to the study
• Have a hemoglobin A1c (HbA1c) of 7.0% to 11.0%, inclusive, at screening
• Have a body mass index (BMI) less than or equal to 45.0 kilograms per square meter (kg/m^2)
• Women of childbearing potential are not breastfeeding, have a negative pregnancy test at screening and randomization, do not plan to become pregnant during the study, have practiced reliable birth control for at least 6 weeks prior to screening and will continue to do so during the study and until 2 weeks after the last dose of study drug

Exclusion Criteria:

• Have used insulin therapy in the past 2 years (except for use during pregnancy or for short term use for acute conditions)
• Have been treated with glucagon-like peptide-1 (GLP-1) receptor agonist, rosiglitazone, pramlintide, or weight-loss medication within 3 months before screening
• For participants on OAMs: have any restrictions for cardiac, renal, and hepatic diseases in the local product regulations
• Are taking, or have taken within the 90 days before screening, prescription or over-the-counter medications to promote weight loss
• Have had any episodes of severe hypoglycemia, diabetic ketoacidosis, or hyperosmolar state/coma within 6 months prior to screening
• Have cardiac disease with functional status that is New York Heart Association Class III or IV
• Have a history of renal transplantation, or are currently receiving renal dialysis or have serum creatinine greater than or equal to 2 milligrams per deciliter (mg/dL) [177 millimoles per liter (mmol/L)]
• Have obvious clinical signs or symptoms of liver disease [excluding non-alcoholic fatty liver disease (NAFLD)], acute or chronic hepatitis, non alcoholic steatohepatitis (NASH), or elevated liver enzyme measurements
• Have had a blood transfusion or severe blood loss within 3 months prior to screening or have known hemoglobinopathy, hemolytic anemia, or sickle cell anemia, or any other traits of hemoglobin abnormalities known to interfere with the measurement of HbA1c
• Have active or untreated cancer, have been in remission from clinically significant cancer(other than basal cell or squamous cell skin cancer) for less than 5 years, or are at increased risk for developing cancer or a recurrence of cancer in the opinion of the investigator
• Are receiving chronic (lasting longer than 14 consecutive days) systemic glucocorticoid therapy (excluding topical, intranasal, intraocular, and inhaled preparations) or have received such therapy within the 8 weeks immediately preceding screening
• Have fasting triglycerides greater than 400 mg/dL (4.5 mmol/L) at screening
• Have an irregular sleep/wake cycle (for example, participants who sleep during the day and work during the night) in the investigator's opinion
• Are using or have used any of the following lipid-lowering medications: niacin preparations as a lipid-lowering medication and/or bile acid sequestrants within 90 days prior to screening