This trial will evaluate the effects of different doses of Lu AG13909 in adult participants with congenital adrenal hyperplasia, also called CAH. CAH is a rare genetic disorder that affects a person's ability to produce certain hormones. The main goals of this trial are to learn about the safety and tolerability of Lu AG13909, how Lu AG13909 behaves in the body, and how the body responds to Lu AG13909.

Inclusion Criteria:

Parts A and B:

• Confirmed diagnosis of 21-hydroxylase deficiency CAH (based on a pathogenic CYP21A2 variant and/or elevated 17-OHP).
• Morning (pre-glucocorticoid [GC] replacement dose) blood concentrations of 17-OHP >4-times upper limit of normal (ULN).
• Body mass index (BMI) ≥18.5 kilograms (kg)/square meter (m^2) (minimum 50 kg) and ≤40 kg/m^2.
• Stable GC replacement therapy for ≥1 month prior to the Screening Visit.
• For the salt-wasting form of CAH, the participant must have been on a stable dose of mineralocorticoid replacement for ≥3 months prior to the Screening Visit.
• Apart from CAH, the participant is generally healthy in the opinion of the investigator and based on medical history, physical examination, vital signs, ECGs, and the results of the safety laboratory tests.

Part C:

• Confirmed diagnosis of 21-hydroxylase deficiency CAH (based on a pathogenic CYP21A2 variant and/or elevated 17-OHP).
• For Cohort C1 only: Morning (pre-GC replacement dose) blood concentrations of androgens (A4) > ULN for age and sex.
• For Cohort C2 only: Morning (pre-GC replacement dose) blood concentrations of androgens (A4) ≤ ULN for age and sex and the participant is treated with high doses of GC.
• Stable GC replacement therapy for ≥1 month prior to the Screening Visit.
• For the salt-wasting form of CAH, the participant must have been on a stable dose of mineralocorticoid replacement for ≥1 month prior to the Screening Visit.

Exclusion Criteria:

• The participant is pregnant or breastfeeding.
• The participant has a clinically significant abnormal laboratory value, electrocardiogram (ECG) parameter, or vital signs value, or other safety findings at the Screening Visit that indicate a potential risk for the participant if enrolled, in the opinion of the investigator.
• The participant has a history of known hypersensitivity or intolerance to Lu AG13909 or its excipients.

Part C Only:

• The participant has received at least one dose of Lu AG13909 in Part A or Part B.

Other inclusion and exclusion criteria may apply.