The primary purpose of this study is to help answer the following research questions:

• To evaluate how much of the study drug (LY2605541) is in the blood of participants with varying degrees of liver impairment compared to those with normal liver function
• To assess the safety of LY2605541 and any side effects that might be associated with it

The study is conducted in 4 groups, based on the Child-Pugh classification of hepatic impairment as follows:

Group 1: Participants with normal hepatic function (Control); Group 2: Participants with mild hepatic impairment (Child-Pugh class A); Group 3: Participants with moderate hepatic impairment (Child-Pugh class B); and Group 4: Participants with severe hepatic impairment (Child-Pugh class C).

Inclusion Criteria:

All Participants (including those with type 2 diabetes mellitus [T2DM] who are controlled by diet)

• Male participants agree to use a reliable method of birth control during the study
• Female participants of child-bearing potential (not surgically sterilized between menarche and menopause) must have a negative pregnancy test at the time of enrollment and must be using a reliable method of birth control
• Women of non-child-bearing potential due to surgical sterilization (at least 6 weeks after surgical bilateral oophorectomy with or without hysterectomy or at least 6 weeks after tubal ligation) confirmed by medical history, or menopause.
• Menopausal women include women with either spontaneous amenorrhea for at least 12 months or spontaneous amenorrhea for 6 to 12 months and a follicle-stimulating hormone (FSH) level greater than 40 milli international units per milliliter (mIU/mL)
• Have a body mass index (BMI) of 18.5 to 40 kilogram per square meter (kg/m^2)
• Have normal sitting blood pressure and heart rate compatible with their disease state
• Have venous access sufficient to allow blood sampling
• Have given written informed consent approved by Lilly and the Ethical Review Board (ERB) governing the site

Participants with Normal Hepatic Function

• Overtly healthy males or females with normal hepatic function
• Have clinical laboratory test results within normal reference range for the investigator site, or results with minor deviations not considered to be clinically significant by the investigator

Participants with Hepatic Impairment

• Have stable liver impairment with no sign of recent deterioration (alcoholic, posthepatitis, biliary cirrhosis, or cryptogenic) classified as Child-Pugh class A, B, or C who are considered by the investigator as acceptable for participation in the study

Exclusion Criteria:

All Participants (including those with T2DM)

• Are currently enrolled in, have completed or discontinued within the last 30 days from a clinical trial involving an investigational product, or are concurrently enrolled in any other type of medical research judged not to be scientifically or medically compatible with this study
• Have an acute infection with fever or infectious disease or febrile illness within 3 days prior to administration of the study medication
• Have known allergies or significant hypersensitivity to LY2605541, its excipients, or related compounds, or history of relevant allergic reactions of any origin
• Have previously completed or withdrawn from this study or any other study investigating LY2605541 and have previously received the investigational product
• Have Type 1 Diabetes Mellitus (T1DM) or have T2DM and are receiving anti-diabetic medication
• Have an abnormality in the 12-lead electrocardiogram (ECG) that, in the opinion of the investigator, increases the risks associated with participating in the study
• Regularly use known drugs of abuse and/or show positive findings on urinary drug screening
• Show evidence of human immunodeficiency virus (HIV) infection and/or positive HIV antibodies
• Have donated blood of more than 500 milliliters (mL) within the last month
• Have had a liver transplant or have taken immunosuppressants following any organ transplant
• Have shown signs of variceal bleeding during the last 2 weeks prior to screening
• Show evidence of irritable bowel syndrome, chronic diarrhea, other symptomatic digestive problems or a known history of repeated chronic stool positive for occult blood, or be considered by the investigator to be at greater risk of acute or chronic pancreatitis
• Have an average weekly alcohol intake that exceeds 21 units per week (males) and 14 units per week (females), or are unwilling to stop alcohol consumption for the duration of the study (1 unit = 12 ounces [oz] or 360 mL of beer; 5 oz or 150 mL of wine; 1.5 oz or 45 mL of distilled spirits)
• Are on total parenteral nutrition
• Take anticoagulants for therapeutic use, other than low dose acetylsalicyclic acid
• Are excessive consumers of xanthines

Participants with Normal Hepatic Function

• Have any medically significant history of neurologic disease, cancer, or cardiac, respiratory, metabolic, hepatic, renal, gastrointestinal (except appendectomy and cholecystectomy), dermatological, venereal, hematological disorder or disease
• Have creatinine clearance (CrCl) less than 80 milliliters per minute (mL/min)
• Show evidence of significant active neuropsychiatric disease in the opinion of the investigator
• Show evidence of hepatitis B and/or positive hepatitis B surface antigen
• Show evidence of hepatitis C and/or positive hepatitis C antibody

Participants with Hepatic Impairment

• Show evidence of any significant active disease other than that responsible for or associated with mild, moderate, or severe hepatic impairment
• Show evidence of hepatorenal syndrome as shown by CrCl <50 mL/min calculated using the Cockcroft-Gault equation
• Have shown signs of spontaneous bacterial peritonitis within 6 months prior to enrollment into the study
• Have severe hyponatremia (sodium <120 millimoles per liter [mmol/L])
• Show signs of hepatocellular carcinoma
• Have a portal shunt
• Show, in the opinion of the investigator, evidence of significant active neuropsychiatric disease other than grade 1 hepatic encephalopathy
• Have hemoglobin concentrations <9.0 grams per deciliter (g/dL)
• Have a platelet count of <30 x 10^9 cells per liter (cells/L), unless, after consultation with the sponsor, they are considered as acceptable for participation in the study
• Have total serum bilirubin concentrations >15 milligrams per deciliter (mg/dL) (>257 micromoles per liter [μmol/L])
• Take medications known to interfere with hepatic metabolism (for example barbiturates or phenothiayines) or known to alter other major organ systems
• Show signs of acute cholestasis or acute cholecystitis
• Have severe ascites

All participants.