A Trial to Test the Safety and Tolerability of Lu AH69593 in Adults That Are Healthy or Have Narcolepsy

Key Inclusion Criteria: For all participants in any trial Part (A, B, C and D): * The participant has a resting supine pulse ≥45 and ≤100 beats per minute (bpm) at the Screening Visit and at the Baseline Visit. Specifically for participants in trial Part A, B, and D: * The participant has a body mass index (BMI) ≥18.5 and ≤30 kilograms (kg)/square meter (m\^2) at the Screening Visit. * The participant has a normal circadian rhythm, defined as a person who usually wakes up between 6:00 and 9:00 a.m. and goes to sleep between 9:00 p.m. and midnight. * The participant is ≥18 and ≤55 years of age at the Screening Visit. Specifically for participants in trial Part C: * The participant has a BMI ≥18.5 and ≤35 kg/m\^2 at the Screening Visit. * The participant has NT1, diagnosed according to International Classification of Sleep Disorders, 3rd edition criteria, with a history of disease diagnosis \>3 months prior to the Screening Visit. * The participant is ≥18 and ≤64 years of age at the Screening Visit. Key Exclusion Criteria: For all participants in any trial Part (A, B, C and D): * The participant has previously been enrolled in this trial. * The participant has previously been dosed with Lu AH69593. * The participant has participated in a clinical trial \<30 days prior to the Screening Visit. * The participant is pregnant, breastfeeding, intends to become pregnant, or is of childbearing potential and not willing to use adequate contraceptive methods. * The participant has a history of cancer, other than basal cell or Stage 1 squamous cell carcinoma of the skin or adequately treated cervical intraepithelial neoplasia, that has not been in remission for \>5 years prior to the first dose of investigational medicinal product (IMP). * The participant has worked shifts, including night duty, or has travelled across \>3 time zones \<2 weeks prior to the first dose of IMP. * The participant trains/exercises intensively, for example, for a marathon or triathlon, or at a competitive level. Specifically for participants in trial Part A, B and D: * The participant has had a clinically significant illness from which he/she recovered \<4 weeks prior to the first dose of IMP. Specifically for Participants in trial Part B and C: * The participant is at significant risk of suicide based on medical history, mental status, investigator judgement, or the C-SSRS answer of 'yes' to suicidal ideation question 4 or 5 or 'yes' to suicidal behaviour, within the last 6 months on the C-SSRS at the Screening Visit or 'Since last visit' at the Baseline Visit Day -1. Specifically for participants in trial Part C: * The participant has any other disorder for which the treatment takes priority over treatment of narcolepsy or is likely to interfere with trial treatment or impair treatment compliance. * The participant has a current medical disorder, other than NT1, associated with excessive daytime sleepiness (EDS). Note: Other protocol-defined inclusion and exclusion criteria may apply.