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

The purpose of this study is to compare LY2605541 and human insulin isophane suspension (NPH) using the following measures for participants treated for up to 26 weeks:

* Change in participants' overall blood sugar control
* The rate of night time low blood sugar episodes
* The number of participants that reach blood sugar targets without low night time blood sugar episodes
* The total number of low blood sugar episodes reported


Eligibility Criteria:
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 \[excluding nonalcoholic fatty liver disease (NAFLD)\], acute or chronic hepatitis, nonalcoholic 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