Inclusion Criteria:

• The participant is a man or woman with a confirmed diagnosis of adrenocorticotropic hormone (ACTH) driven CD of pituitary source as per current guidelines

• Morning plasma ACTH levels > lower limit of normal (LLN) and

• Evidence of a pituitary origin of the excess ACTH:

  i. Either MRI confirmation of pituitary adenoma >6 millimeters (mm), or ii. inferior petrosal sinus gradient >2, or iii. histopathology confirmation of ACTH-secreting tumour

• The participant has a 24-hour UFC >1.5 × ULN (the mean of ≥3 days of 24-hour urine collection).

• Apart from CD and associated well-controlled comorbidities (for example, diabetes mellitus and hypertension), the participant is generally healthy in the opinion of the investigator and based on medical history, physical examination, vital signs, electrocardiogram (ECG), and the results of the safety laboratory tests.

• For participants on medical treatment for hypercortisolism due to CD, pre-defined washout periods must be completed prior to the Baseline efficacy assessments.

Exclusion Criteria:

• 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 a clinically significant abnormal laboratory value, ECG parameter, vital signs value, or other safety findings at the Screening Visit that indicate a potential risk to the participant's safety if enrolled, in the opinion of the investigator.

• The participant has a history of known hypersensitivity or intolerance to Lu AG13909 or its excipients.

• The participant has immediate need for pituitary surgery within 6 months from screening in the opinion of the investigator.

• The participant has severe CD per investigator judgement; among others, this could be participants with:

  i. poorly controlled hypertension ii. poorly controlled diabetes mellitus iii. severe psychiatric illness iv. compression of the optic chiasm causing any visual field defect or risk thereof v. very high risk of thromboembolic events

• The participant had pituitary surgery <3 month prior to screening.

• The participant had pituitary radiotherapy within the last 10 years.

Other protocol-defined criteria apply.