Current efforts towards a more fundamental theory beyond the Standard Model of Particle Physics open up a window for deviations from exact Lorentz symmetry. To test Lorentz symmetry, one can make use of the extreme energies reached by ultra-high-energy cosmic rays (UHECRs), which are far beyond what is accessible by other means. We use the air showers initiated by UHECRs in the Earth’s atmosphere to study the effects of Lorentz violation (LV), focusing on isotropic, non-birefringent LV in the photon sector. New processes, which are forbidden in case exact Lorentz symmetry holds, can significantly change the shower development. One such process is vacuum Cherenkov radiation, a very efficient energy-loss process for charged particles such as electrons and positrons. We primarily focus on the average depth of the shower maximum $\langle X_\text{max}\rangle$ and its shower-to-shower fluctuations $\sigma(X_\text{max})$, which we study using air-shower simulations. Comparing our results to measurements, we obtain a new upper bound on the key LV parameter $\kappa$, which improves the previous bound by a factor of 2. This is the first bound based on vacuum Cherenkov radiation from fundamental particles in air showers. This result also complements previous bounds on $\kappa < 0$. Also here, our approach - then involving photon decay instead of vacuum Cherenkov radiation - led to the world’s best bound on $\kappa$. In addition to summarizing these results, we explore related changes in the muonic shower component, which may lead to further improvements.