The main purpose of this study is to evaluate the safety and tolerability of LY3549492 in participants with T2DM. Blood tests will be done to check how much LY3549492 gets into the bloodstream and how the body handles LY3549492. This study has two parts. Each participant will enroll in only one part. The study will last either 12 or 13 weeks, depending on part.

Inclusion Criteria:

• Participants with T2DM for at least 6 months, as defined by the American Diabetes Association or the World Health Organization,

  • treated with diet and exercise and stable dose(s) of metformin, with or without 1 other oral antidiabetic medication (OAM) at stable dose, 3 months prior to study entry

  • If taking statins, must be on stable statin treatment without a history of statin myopathy for at least 3 months

  • with a glycated hemoglobin (HbA1c) value of

    • greater than or equal to (≥)6.5 percent (%) and less than or equal to (≤)10.5% at screening on metformin only and
    • ≥6.5% and ≤9.5% on metformin in combination with OAMs other than metformin.

• Body weight ≥45.0 kilograms (kg) and body mass index within the range of 18.5 to 45.0 kilogram per square meter (kg/m²) (inclusive).

• Stable body weight for the 3 months prior to screening

• Women must not be of childbearing potential.

Exclusion Criteria:

• Women of childbearing potential.

• Have type 1 diabetes mellitus, known latent autoimmune diabetes in adults, or have had an episode of ketoacidosis or hyperosmolar state requiring hospitalization in 6 months prior to screening.

• Have active proliferative diabetic retinopathy, diabetic maculopathy, or severe nonproliferative diabetic retinopathy that requires acute treatment

• Present with uncontrolled comorbid conditions commonly associated with diabetes (for example, hypertension, hypercholesterolemia) or have had changes to medication for those conditions within 1 month prior to screening.

• Have had an episode of severe hypoglycemia, as defined by the occurrence of neuroglycopenic symptoms requiring the assistance of another person for recovery, within 6 months prior to screening visit, or have a history of hypoglycemia unawareness or poor recognition of hypoglycemic symptoms. Any participant that the investigator feels will not be able to communicate an understanding of hypoglycemic symptoms and the appropriate treatment of hypoglycemia should also be excluded.

• Have a known clinically significant gastric emptying abnormality (for example, severe diabetic gastroparesis or gastric outlet obstruction), have undergone gastric bypass (bariatric) surgery or restrictive bariatric surgery (for example, gastric banding ), and/or device-based therapy for obesity, or have had device removal within the past 6 months.

• Have active or symptomatic gastric ulceration or chronic gastritis.

• Have evidence of hypothyroidism or hyperthyroidism based on clinical evaluation or an abnormal thyroid stimulating hormone (for those with current or previous thyroid history) that, in the opinion of the investigator, would pose a risk to participant safety.

• Have known definitive diagnosis of autonomic neuropathy as evidenced by neuropathic urinary retention, resting tachycardia, orthostatic hypotension, or diabetic diarrhea.

• Have obesity induced by other endocrine disorders such as Cushing's syndrome or Prader-Willi syndrome.

• A history of additional risk factors for Torsades de Pointes (for example, heart failure, hypokalemia, family history of long QT syndrome, use of concomitant medications that prolong the QT/QTc interval).

• Have an abnormality in the 12-lead electrocardiogram (ECG) at screening that, in the opinion of the investigator, increases the risks associated with participating in the study or may confound ECG data analysis

• Have a significant history (within the past 6 months) of or current comorbidities capable of altering the absorption, metabolism, or elimination of drugs; of constituting a risk when taking the study drug; or of interfering with the interpretation of data. These include cardiovascular, respiratory diseases, renal diseases, gastrointestinal (GI) diseases, hematological diseases, neurological diseases, dermatological diseases

• Have a history or presence of pancreatitis (history of chronic pancreatitis or idiopathic acute pancreatitis), elevation in serum amylase or lipase levels (>2.5 fold the upper limit of normal [ULN]).

• Have a personal or family history of medullary thyroid carcinoma or multiple endocrine neoplasia syndrome type 2.

• Have a serum calcitonin level of

  • ≥20.0 picograms per milliliter (pg/mL) at screening, if estimated glomerular filtration rate is ≥60 milliliters per minute per 1.73 m² (mL/min/1.73 m²)
  • ≥35.0 pg/mL at screening, if estimated glomerular filtration rate is <60 mL/min/1.73 m²

• Have known liver disease, obvious clinical signs or symptoms of liver disease, acute or chronic hepatitis, or have elevations in aminotransferases (alanine transaminase [ALT] and aspartate aminotransferase [AST]) greater than 2 × ULN.

• Have total bilirubin level (TBL) >1.5 × ULN (except for participants diagnosed with Gilbert's syndrome).