The purpose of this study is to evaluate the safety, tolerability, and pharmacokinetics/pharmacodynamics (PK/PD) of LY3962681 in healthy volunteers and patients with Parkinson's disease.

The study consists of two parts, the Single Ascending Dose (SAD) study and the Multiple Ascending Dose (MAD) study.

During the SAD portion of the study, healthy volunteers will receive a single dose of LY3962681 or placebo (artificial cerebrospinal fluid [aCSF]) administered intrathecally (into the spinal fluid). During the MAD portion of the study, patients with Parkinson's disease will receive two doses of either LY3962681 or placebo (aCSF) administered intrathecally (into the spinal fluid), 12 to 24 weeks apart.

• The treatment period in the SAD study will be 1 day. The treatment period in the MAD study will be 2 dosing days, 12 to 24 weeks apart.
• The follow-up period in the SAD study will be up to 52 weeks. The follow-up period in the MAD study will be up to 52 weeks after Dose 2.

Inclusion Criteria:

• Participant is overtly healthy as determined by medical evaluation. Rescreening is allowed in this study.
• A Montreal Cognitive Assessment score greater than or equal to 24.
• Stable use of background medications at least 8 weeks prior to IP administration, including but not limited to those used for treatment of Parkinson's disease (including deep brain stimulation), and the investigator must expect that participant can tolerate a minimum of 6 months without dose adjustment.

MAD study only

• Participant has a diagnosis of Parkinson's disease per UK Parkinson's Disease Society Brain Bank Clinical Diagnostic Criteria.
• Modified Hoehn and Yahr Stage 1 to 2.5 in the practically defined OFF state.
• A positive result on CSF alpha-synuclein Seed Amplification Assay. (A prior positive result [within 1 year of screening] accepted with sponsor approval if patient did not participate in another Parkinson's disease clinical trial during this period.) (US and Japan only)
• UPSIT score of 20 percentile or less, corrected for age and sex (EU and UK only).
• An abnormal DaT-SPECT consistent with parkinsonism. (History of an abnormal DaTSPECT with the report confirmed by study investigator will be accepted.)
• For participants not taking Parkinson's disease medications, not expected to initiate treatment within 6 months.
• Have a body weight within 40 kg (88 pounds) to 110 kg (242 pounds), inclusive, and body mass index within the range of 17 to 34 kg/m^2, inclusive.

Exclusion Criteria:

• MAD study only: Significant neurological disease affecting the central nervous system other than Parkinson's disease that may be a cause for the participant's clinical symptoms or may confound study objectives.
• Current concomitant disease or serious or unstable illnesses, including central nervous system (SAD study only), cardiovascular, hepatic, renal, gastroenterology, respiratory, endocrinologic, neurologic (MAD study only: other than Parkinson's disease), psychiatric, immunologic, or hematologic disease and other conditions that, in the investigator's opinion, could interfere with the conduct of the study or that would, in the opinion of the investigator, pose an unacceptable safety risk to the participant.
• Participant is generally frail or has any medical disorders that, in the opinion of the investigator, could interfere with study-related procedures (including safe performance of IT injection or LP), such as prohibitive spinal diseases, bleeding diathesis, clinically significant coagulopathy, thrombocytopenia, or increased intracranial pressure.
• Have a 12-lead 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.
• MAD study only: Treatment with continuous intestinal delivery Parkinson's disease medication (for example, Duodopa).
• MAD study only: Significant renal impairment (estimated glomerular filtration rate [eGFR] <45 mL/min/1.73 m^2).

Other protocol-defined inclusion/exclusion criteria may apply.

Both the SAD and MAD studies are double blinded (sponsor unblinded); that is, both the participants and the site personnel are blinded to the study intervention.