Yes. Your child can still be vaccinated if they have asthma. Please mention it to the healthcare professional on the day of vaccination, in case of updated medical advice.
LAIV (nasal flu spray) is not recommended for children and adolescents currently experiencing an acute exacerbation of symptoms (those who have had increased wheezing or needed additional inhaler use in previous 72 hours). These children can delay vaccination until fit or a flu injection could be offered.