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

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