A Study in Participants With Type 2 Diabetes Mellitus

The purpose of this study is:

* To compare blood glucose (blood sugar) control on LY2605541 with insulin glargine after 26 weeks of treatment.
* To compare the rate of night time hypoglycemia (low blood glucose) on LY2605541 with insulin glargine during 26 weeks of treatment.
* To compare the number of participants on LY2605541 reaching blood glucose targets without hypoglycemia episodes at night to those taking insulin glargine after 26 weeks of treatment.
* To compare the rate of hypoglycemia over a 24-hour period on LY2605541 with insulin glargine during 26 weeks of treatment.


Eligibility Criteria:
Inclusion Criteria

* Have type 2 diabetes mellitus based on the World Health Organization (WHO) classification
* Had diabetes ≥1 year
* Have a hemoglobin A1c (HbA1c) value ≥7.0% and \<12.0% at screening
* Have a body mass index (BMI) ≤45.0 kilograms per square meter (kg/m\^2)
* Participants on any glucose lowering regimen that contains at least 1 daily insulin injection
* This inclusion criterion applies ONLY to women of childbearing potential

  * Are not breastfeeding
  * Test negative for pregnancy at screening and randomization
  * Do not intend to become pregnant during the study
  * Have practiced a reliable method of birth control for at least 6 weeks prior to screening
  * Agree to continue to use a reliable method of birth control during the study, as determined by the investigator (and for 2 weeks following the last dose of study drug)
* Have access to a method of communication with the site
* Have refrigeration in the home
* Capable of, and willing to do the following: adhere to a multiple daily injection regimen, inject insulin with a covered vial and syringe and prefilled pen, attend some appointments in the fasting state, and perform self blood glucose monitoring and record keeping as required by this protocol, as determined by the investigator. Caregiver may be responsible for all of the above
* Have given written informed consent to participate in this study in accordance with local regulations

Exclusion Criteria

* Continuous subcutaneous insulin infusion therapy prior to screening
* Are using twice daily insulin glargine prior to screening
* Excessive insulin resistance defined as having received a daily dose of insulin ≥2.0 units per kilogram (units/kg) at the time of pre-randomization
* Glucagon-like peptide-1 (GLP-1) receptor agonist (eg, exenatide, exenatide once weekly, or liraglutide), thiazolidinedione (rosiglitazone, pioglitazone), or pramlintide, used concurrently or within 90 days prior to screening
* Are using niacin preparations as a lipid-lowering medication and/or bile acid sequestrants within 90 days prior to screening; or, are using lipid-lowering medication at a dose that has not been stable for ≥90 days prior to screening
* Have fasting hypertriglyceridemia (defined as \>4.5 millimoles per liter \[mmol/L\], \>400 milligrams per deciliter \[mg/dL\]) at screening
* Are currently taking, or have taken within the 90 days preceding screening, prescription or over-the-counter medications for weight loss
* Have had any episode of severe hypoglycemia (defined as requiring assistance due to neurologically disabling hypoglycemia) within 6 months prior to entry into the study
* Have had 2 or more emergency room visits or hospitalizations due to poor glucose control within the 6 months prior to screening
* Have had 1 or more episodes of ketoacidosis or hyperosmolar state/coma requiring hospitalization within 6 months prior to screening
* Have cardiac disease with functional status that is New York Heart Association Class III or IV (per New York Heart Association Cardiac Disease Classification)
* Are currently receiving renal dialysis or have a serum creatinine ≥2.0 mg/dL, except for participants taking metformin who will be required to follow local labeling restrictions regarding metformin use and serum creatinine
* 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 as indicated below:

  * total bilirubin ≥2X the upper limit of normal (ULN) as defined by the central laboratory, or
  * alanine aminotransferase (ALT)/serum glutamic pyruvic transaminase (SGPT) \>2.5X ULN as defined by the central laboratory, or
  * aspartate aminotransferase (AST)/serum glutamic oxaloacetic transaminase (SGOT) \>2.5X ULN as defined by the central laboratory
* Have active or untreated malignancy, have been in remission from clinically significant malignancy (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
* Have known or develop hypersensitivity or allergy to any of the study insulins or their excipients
* 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 HbA1c measurement
* Receiving chronic (lasting longer than 14 consecutive days) systemic glucocorticoid therapy (excluding topical, intraocular, intranasal, and inhaled preparations) or have received such therapy within 8 weeks immediately before screening with the exception of replacement therapy for adrenal insufficiency
* Diagnosed clinically significant diabetic autonomic neuropathy, in the opinion of the investigator
* Have had an organ transplant
* Have any other condition (including known drug or alcohol abuse or psychiatric disorder including eating disorder) that precludes the participant from following and completing the protocol