Lightning strokes emit electromagnetic pulses that interact with the lower ionosphere. One manifestation of this interaction are elves: ring-shaped light emissions from altitudes around 85 km above active thunderstorms. Perturbations to the conductivity at those altitudes relax with time-scales longer than ten minutes and therefore one strong pulse may affect the features of subsequent pulses. Here we develop a simplified model to investigate this possibility. We apply this model to thunderstorms with a copious production of high-peak-current strokes. We conclude that this interaction is indeed possible and may affect the properties of elves at different stages of a thunderstorm.