A Study of LY3872386 in Healthy Participants and Participants With Atopic Dermatitis

Inclusion Criteria: Part A and C: * Overtly healthy as determined by medical evaluation 1. To qualify as Japanese for the purpose of this study, the participant must be first generation Japanese, defined as the participant's biological parents and all of the participant's biological grandparents must be of exclusive Japanese descent, and must have been born in Japan 2. To qualify as Chinese for the purpose of this study, the participant must be, at a minimum, third-generation Chinese, defined as all 4 of the participant's biological grandparents must be of exclusive Chinese descent and born in China * Have a body mass index of 18.0 to 32.0 kilograms per square meter (kg/m²), inclusive * Male participants who agree to use highly effective or effective methods of contraception and women not of childbearing potential may participate in part A and C Part B: * Participants who have a diagnosis of atopic dermatitis at least 12 months prior to screening as defined by the American Academy of Dermatology * Have a history, documented by a physician and/or investigator, of inadequate response to existing topical medications within 6 months preceding screening, or participants who failed systemic therapies intended to treat atopic dermatitis or a history of intolerance to topical therapy * Have a body mass index of 18.0 to 38.0 kilograms per square meter (kg/m²), inclusive * Male participants who agree to use highly effective or effective methods of contraception, women not of childbearing potential and women of childbearing potential may participate in part B Exclusion Criteria: * Women who are pregnant and/or lactating * Participants who have received live vaccine(s) (including attenuated live vaccines) or Bacillus Calmette- Guérin within 35 days of screening * Have a history or presence of multiple or severe allergies or an anaphylactic reaction to prescription or nonprescription drugs * Have a known history of diabetes * Have fasting glucose level of ≥126 milligrams per deciliter (mg/dL) and glycated hemoglobin ≥6.5 percent (%) and/or taking anti-diabetes medications at screening * Have known history of osteoporosis