The prototype Large-Sized Telescope (LST-1) of the Cherenkov Telescope Array Observatory (CTAO) is in commissioning phase at the Observatorio del Roque de Los Muchachos at 2200 m
a.s.l. in La Palma (Canary Islands, Spain). LST-1 is a 23-m diameter telescope and is the first of four that will compose the LST part of the CTAO Northern array. The LST subarray is optimized to provide the best sensitivity for gamma rays in the 20 GeV - 200 GeV energy range. The MAGIC
telescopes, which are located approximately 100 m from the LST-1, is operating as a two 17-m telescope stereoscopic system for more than 14 years. LST-1 and MAGIC routinely perform joint observations of gamma-ray sources to exploit the potential of the three-telescope system. This contribution describes the analysis pipeline and evaluates the performance of the system using Monte Carlo simulations and data on the Crab Nebula. The sensitivity achieved during joint observations with MAGIC and LST-1 is about 30% higher than that of MAGIC alone.