A Trial to Learn More About Repeated Monthly Injections of Lu AG09222 in Participants With Allergies to Grass Pollen

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 card…