This trial will evaluate the effects of Lu AF28996 in adults with Parkinson's disease (PD) experiencing motor fluctuations despite optimized non-invasive symptomatic treatment. These are individuals with PD who take medications to control movement symptoms, such as slowness, stiffness, and tremor, but still experience periods of time when their medication does not adequately control their motor symptoms. Some may also experience dyskinesia (other type of involuntary movements) as a side effect of their PD medications. The main goal of the trial is to learn whether adding Lu AF28996 to participants' optimized PD medications will help extending the time they spend with their movement symptoms being well-controlled and without bothersome dyskinesia.

Key Inclusion Criteria:

• The participant was diagnosed with PD ≥3 years ago, with the diagnosis being established after the age of 30 years and consistent with the Movement Disorders Society (MDS) Clinical Diagnostic Criteria for "clinically established" or "clinically probable" PD.
• The participant has a modified Hoehn and Yahr scale (mH&Y) stage ≤3 in the ON state and ≥2 and ≤4 in the OFF state.
• The participant reports well recognizable, consistent motor fluctuations causing significant disability per investigator's judgement over a period of ≥3 months prior to screening.
• The participants report motor fluctuations each day as measured by OFF-time during awake hours.

Key Exclusion Criteria:

• The participant has previously been dosed with Lu AF28996.
• The participant has participated in a clinical trial <30 days prior to screening.
• The participant is pregnant, breastfeeding, intends to become pregnant, or is of child-bearing potential and not willing to use adequate contraceptive methods.
• The participant has taken any investigational medicinal product (IMP) <3 months or <5 half-lives, whichever is longer, prior to screening.
• The participant has a Montréal Cognitive Assessment (MoCA) score ≤24 (adjusted for education).
• The participant has an atypical, secondary, or drug-induced Parkinsonism (for example, metoclopramide, flunarizine), metabolic identified neurogenetic disorders (for example, Wilson's disease), encephalitis, or Parkinson Plus syndromes or other forms of atypical Parkinsonian syndromes (for example, progressive supranuclear palsy and multiple system atrophy).
• The participant has severe, pervasive, disabling dyskinesia which, in the setting of the present trial, may interfere with his/her safe participation in the trial (for example, threat to falling, aspiration, etc.) as judged by the investigator.
• The participant has unpredictable motor fluctuations as evidenced by an MDS-UPDRS Part IV Item 4.5 score ≥3 at screening and/or experiences wide, unpredictable fluctuations of PD symptoms per investigator's clinical judgement.

Note: Other protocol defined inclusion and exclusion criteria may apply