The main purpose of this study is to explore the safety and any side effects of LY4066708 in healthy participants. The study will also measure how much LY4066708 gets into the bloodstream and the central nervous system and how long it takes the body to remove it. The study will last up to 24 weeks for each participant.

Inclusion Criteria:

• Are overtly healthy as determined by medical evaluation including medical history, physical examination, laboratory tests, and cardiac monitoring.
• Japanese Participants Only: To qualify as a participant of first-generation Japanese origin, the participant, the participant's biological parents, and all the participant's biological grandparents must be of exclusive Japanese descent and born in Japan.
• Chinese Participants Only: To qualify as Chinese for the purpose of this study, all 4 of the participants' biological grandparents must be of exclusive Chinese descent and born in China, Hong Kong, Macau, or Taiwan.
• Have a body mass index (BMI) at the time of screening within the range 18.5 to 30 kilogram per meter squared (kg/m²) (inclusive).
• Participants assigned female at birth (AFAB) not of childbearing potential and participants assigned male at birth (AMAB) willing to practice effective contraception throughout the study may participate.
• Willingness to undergo study procedures which may include repeated lumbar punctures

Exclusion Criteria:

• Are individuals of childbearing potential (IOCBP). Notwithstanding their IOCBP status, participants AFAB are excluded if they are breastfeeding.
• A history of additional risk factors for Torsades de Pointes (for example, heart failure, hypokalemia, family history of Long QT Syndrome).
• The use of concomitant medications that prolong the QT/QTc interval.
• Have known allergies to LY4066708 or any components of the formulation, or history of allergic reactions to any transferrin receptor (TfR) antibodies.
• Have participated, within the 3 months of screening, in a clinical trial involving a study intervention (other than the study intervention used in this study). If the previous investigational product has a long half-life (t½), 3 months or 5 half-lives (whichever is longer) should have passed.
• Are persons who have previously completed or withdrawn from this study and have previously received the study intervention. This exclusion criterion does not apply to subjects who are allowed to rescreen prior to randomization.
• Have a 12-lead electrocardiogram (ECG) abnormality at screening that, in the opinion of the investigator, increases the risks associated with participating in the study, or may confound ECG data analysis.
• Show evidence of hepatitis C and/or positive hepatitis C antibody.
• Current infection with hepatitis B virus (HBV) or evidence of past infection with HBV, that is, positive for Hepatitis B surface antigen (HBsAg) or Hepatitis B core total antibody (anti-HBc).
• A marked baseline prolongation of time from the start of the Q wave to the end of the T wave/ corrected QT interval (QT/QTc) interval (for example, repeated demonstration of a corrected time from the start of the Q wave to the end of the T wave interval - Fridericia formula (QTcF) interval greater than 450 ms).