The next generation facility for gamma-ray ground-based observations is the Cherenkov Telescope Array (CTA) observatory, which comprises three types of imaging atmospheric Cherenkov telescopes (IACTs). The Large-Sized Telescopes (LSTs) of CTA are the largest telescope type with a mirror dish of 23 m diameter. They cover the low energy end of the accessible gamma-ray energies for IACTs, starting from about 20 GeV up to a few TeV. The first LST prototype, known as LST-1, was officially inaugurated at the Observatorio del Roque de Los Muchachos in La Palma (Canary Islands, Spain) in 2018 and has since performed calibration observations of various known gamma-ray sources. Additionally, the site houses the MAGIC telescopes, two 17 m IACTs situated approximately 100 m away from LST-1, which have been performing stereo observations since 2009. Currently, joint observations between LST-1 and MAGIC are being carried on, and the data taken independently by the two IACT systems is analyzed by combining events via software. However, this method increases the energy threshold, as it discards all but the relatively high-energy events triggered by all three telescopes. To address this issue, we have developed a novel hardware stereo trigger system between LST-1 and MAGIC, which is capable of handling events triggered by any-two out of the three telescopes. In this contribution, we will report on the performance estimation of joint LST-1 and MAGIC observations using the hardware trigger.