• Participants diagnosed with idiopathic PD (consistent with the UK PD Society Brain Bank Criteria for the Diagnosis of PD), with not more than 1 first-degree relative who has PD.

• Participants must have a Modified Hoehn and Yahr score ≤4 in the OFF state and ≤3 in the ON state, and a Mini Mental State Examination score \>25.

• The OFF/ON amplitude on the MDS-UPDRS Part III at screening must be minimum 30% difference.

• Participants must experience recognizable and predictable motor fluctuations (with at least 1.5 hours of OFF periods in the awake time, including predictable morning OFF episodes), causing clinically significant disability during the 7-week Screening Period, as evaluated by the investigator. This will be documented using a participant ON/OFF state registration over 3 consecutive days prior to enrolment.

• Allowed concomitant medication for PD during the study includes levodopa, monoamine oxidase B inhibitors, COMT inhibitors, anticholinergics, and amantadine. Dopamine agonists are not allowed and should be discontinued ≥4 weeks prior to dosing with Lu AF28996 and until the end of the study.

• Participants diagnosed with idiopathic PD (consistent with the UK PD Society Brain Bank Criteria for the Diagnosis of PD), with not more than 1 first-degree relative who has PD.

• Participants must have a Modified Hoehn and Yahr score ≥2 to ≤4 in the OFF state and ≤3 in the ON state, a MDS-UPDRS Part IV, 4.5 score of 1 or 2, and a MDS-UPDRS Part IV, 4.2 score ≥2 (at least mild functional impact), and a Mini Mental State Examination score \>25 at the Screening Visit.

• Participants must currently have a good response to levodopa and be receiving a stable dose of levodopa (≥3 doses per day of levodopa/dopa decarboxylase inhibitor therapy or ≥3 doses per day of levodopa Extended-Release Capsules and LEDD between 400 and 1600, inclusive) for at least 4 weeks prior to screening.

• Participants must experience recognizable and predictable motor fluctuations (with ≥3 hours of OFF periods in the awake time, including predictable morning OFF episodes), causing clinically significant disability during 3 months prior to enrolment, as evaluated by the investigator. The criteria will be documented using Hauser Diary over 3 consecutive days prior to enrolment.

• Participants must experience ≥1 hour daily ON time with troublesome dyskinesia (TD) in the awake time (TD/24 hours while awake) during the last 3 months prior to enrolment as evaluated by the investigator. The criteria will be documented using the Hauser Diary over 3 consecutive days prior to enrolment.

• Allowed concomitant medication for PD during the study includes levodopa, dopamine agonists, if allowed daily dose, monoamine oxidase B inhibitors, COMT inhibitors, anticholinergics, and amantadine.