A Study of LY2605541 in Participants With Type 2 Diabetes Mellitus

The purpose of this study is to compare LY2605541 and insulin glargine using the following measures after participants have been treated for 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 blood sugar episodes at night
* The rate of low blood sugar episodes reported over a 24-hour period


Eligibility Criteria:
Inclusion Criteria:

* Have had type 2 diabetes mellitus for at least 1 year
* Have been receiving basal insulin (neutral protamine Hagedorn \[NPH\], detemir, or glargine) and a stable dose of 0 to 3 oral antihyperglycemic medications (OAMs) used as specified in the local prescribing information for at least 90 days prior to screening. At least 1 of the OAMs must be dosed at, or above, half the maximum daily dose allowed by local regulations or at the maximally tolerated dose
* Have a hemoglobin A1c (HbA1c) less than or equal to 9.0% 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 who are not breastfeeding, have a negative pregnancy test at screening and randomization, do not plan to become pregnant during the study, and 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 routinely used insulin glargine twice daily in the 90 days prior to the study or have used routine, mealtime insulin therapy (outside of pregnancy) anytime in the past 6 months, except for short-term treatment up to a maximum of 4 continuous weeks
* Have used rosiglitazone, pramlintide, glucagon-like peptide 1 (GLP-1) receptor agonist concurrently or within 90 days prior to 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 preceding screening, prescription or over-the-counter medications to promote weight loss
* Have had any episodes of severe hypoglycemia within 6 months prior to screening
* Have had 1 or more episodes of diabetic ketoacidosis or hyperosmolar state/coma in the 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 micromoles per liter \[µmol/L\])
* 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 millimoles per liter \[mmol/L\]) 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
* Lipid-lowering medication: Are using or have used any of the following:

  * niacin preparations as a lipid-lowering medication and/or bile acid sequestrants within 90 days prior to screening or
  * lipid-lowering medication at a dose that has not been stable for at least 90 days prior to screening