A Study of LY4167586 in Participants With Obesity or Overweight With or Without Type 2 Diabetes

Inclusion Criteria: * Participants must be 21 in Singapore. * Have had a self-reported stable weight for 3 months prior to screening (less than approximately 5 percent (%) body weight change. Part A, B, D, and E * Have a body mass index (BMI) of greater than or equal to 30 kilograms per square meter (kg/m²) or 27 to less than 30 kg/m² and previously diagnosed with at least one of the following weight-related comorbidities: * hypertension * dyslipidemia * obstructive sleep apnea, or * prediabetes. Part C * Have a BMI ≥25.0 kg/m² * Have a diagnosis of Type 2 Diabetes (T2D) for at least 6 months. * T2D controlled with diet and exercise alone or are on a stable dose of metformin alone, or in combination with a sodium-glucose co-transporter-2 inhibitor (SGLT-2i), for at least 3 months. * Have a hemoglobin (HbA1c) value of ≥6.5 % and ≤10.0%. Part D * To qualify as Chinese for this study, the participant must be at a minimum third-generation Chinese, defined as having all 4 of the participants' biological grandparents being of exclusive Chinese descent and born in China. Part E * To qualify as Japanese for this study, the participant must be at a minimum third-generation Japanese, defined as having all 4 of the participants' biological grandparents being of exclusive Japanese descent and born in Japan. Exclusion Criteria: * Have a significant history or presence of cardiovascular, respiratory, hepatic, renal, gastrointestinal (GI), endocrine (except for T2D in Part C), hematological, or neurological disorders capable of significantly altering the absorption, metabolism, or elimination of drugs, or of constituting a risk when taking the study drug, or of interfering with the interpretation of data.