The main goal of this trial is to learn more about the safety of repeated dosing with Lu AG09222. The trial doctors will keep track of the participant's overall health by asking them how they are and by analyzing blood and urine samples.

Inclusion Criteria:

• The participant has a body mass index (BMI) ≥18.0 and ≤30 kilograms (kg)/square meter (m^2) at the screening visit.
• The participant has a clinical history of grass pollen allergic rhinitis of at least 2 years' duration as diagnosed by a physician.
• The participant has a positive specific immunoglobulin E (IgE) (defined as ≥class 2, ≥0.70 kilounits [kU]/liter [L]) against Phleum pratense at screening.
• The participant has a positive skin prick test with a wheal size ≥3 mm to Phleum pratense at screening.
• The participant is, in the opinion of the investigator, generally healthy based on medical history (despite the allergic rhinitis), a physical examination, vital signs, an electrocardiogram (ECG), and the results of the clinical chemistry, haematology, urinalysis, serology, and other laboratory tests.

Exclusion Criteria:

• The participant has received sublingual or subcutaneous immunotherapy with Phleum pratense within the last 5 years.
• The participant is receiving ongoing treatment with any allergy immunotherapy product.
• The participant has a clinically relevant history of symptomatic (seasonal or perennial) allergy caused by an allergen source overlapping with the allergen challenge period.
• The participant has taken disallowed medication or received a COVID-19 vaccination within the protocol-specified amount of time before Day 1.
• The participant has a relevant history of systemic allergic reaction, for example anaphylaxis with cardiorespiratory symptoms, generalized urticaria, or severe facial angioedema, which in the opinion of the investigator may constitute an increased safety concern.

Other inclusion and exclusion criteria may apply.