The Cherenkov Telescope Array Observatory (CTAO) is the next generation of observatory employing the imaging air Cherenkov technique for the study of very high energy gamma rays in the range from 20 GeV to 300 TeV. The first full CTAO telescope, the LST-1, is operational in La Palma, and is acquiring data that has achieved the identification of established sources, exploration of unknown ones, and validation of anticipated performance benchmarks. The deployment of deep learning methods, thanks to the GammaLearn project, for the reconstruction of physical attributes of incident particles, encompassing parameters like energy, arrival direction, and particle classification, has evinced promising outcomes when conducted on simulations. However, the transition of this approach to observational data is accompanied by challenges, as deep learning-based models are susceptible to domain shifts. In the present contribution, we address this issue through the integration of domain adaptation into state-of-the-art deep learning models, and we shed light on the performance that they bring using LST-1 data.