The ice phase is a major contributor to precipitation formation over continents due to its efficiency in growing hydrometeors to large enough sizes for sedimentation. One prominent growth mechanism is the vapor deposition onto ice crystals. However, its actual growth rates remain ambiguous. In the CLOUDLAB project, we conducted field experiments in supercooled clouds with the goal to infer ice crystal growth rates through local perturbations from cloud seeding. In this study, we combine the high-resolution model setup of 65\,\unit{m} with Lagrangian trajectories to achieve a more straightforward comparison to the observations. We first show that the chosen field experiments can be reproduced in the model in terms of ice crystal number concentration. Second, we perform a series of sensitivity studies by perturbing two parameters in the vapor depositional growth equation. The goal is to understand what change is needed to achieve an agreement between simulated and observed ice crystal growth rates since the default model configuration fails to do so. Increasing the vapor deposition efficiency by a factor of up to 3 yields comparable growth rates to the observations. Last, we try to quantify the different contributions to the vertical motions within the seeding plume, such as the large-scale forcing, the underlying topography, and latent heat release upon ice nucleation and growth. We show the different factors are superposed with the large-scale forcing being a dominant factor. The Lagrangian trajectories proved to be crucial to bridge dynamics and cloud microphysical processes.