Predictive numerical capabilities have the potential for significant impact in the advancement of therapies for lung disease. Accurate and efficient numerical models can provide a valuable clinical aid to optimise therapies and to define the appropriate treatment, for example in severe asthma and chronic obstructive pulmonary disease (COPD). Geometric variations of the respiratory airways across subjects, however, have a pronounced effect on the airflow and aerosol deposition and, hence, pose a significant hurdle which motivates personalised treatment of respiratory diseases. An in silico framework for patient-specific predictions of the flow and aerosol deposition in the respiratory airways is presented. The proposed computational laboratory efficiently accommodates geometric variation and airway motion in order to optimise pulmonary delivery for patients with severe asthma and COPD. Dynamic airway models conforming to the patient’s breathing are constructed via a non-rigid registration method. The flow solver takes advantage of a novel immersed boundary (IB) approach which efficiently handles realistic airway geometries obtained from medical images of patients’ lungs. The transport and deposition of the aerosol particles in the airways is modelled via a Lagrangian point particle-tracking scheme. Using this method, the flow and aerosol deposition in realistic extrathoracic airways are examined and a patient-specific dynamic lung model is presented.