In recent years, following the first detection of Gravitational Waves (GWs), we have witnessed the birth of GW Astronomy. So far, there have been a plethora of events recorded, providing us with invaluable information about the very nature of the merging binaries. An exceptional case is the event GW170817, a Neutron Star merger, which was observed with both gravitational and electromagnetic (EM) waves. From a single event alone, by combining both ways of observation, we were able to vastly improve our understanding of such cataclysmic events. In the near future, in particular, in the early 2030s, the ESA Laser Interferometer Space Antenna (LISA) is going to be launched. LISA is a space-borne Gravitational-Wave observatory that, in contrast to the present ground-based detectors, is going to be signal-dominated. The LISA data will give us the unique opportunity to observe different types of GW events, from the merger of supermassive black hole binary systems to Double White Dwarfs. Some of those signals could be potentially combined with the EM observations emitted by the same event. This complementarity of information will enable us to push our knowledge boundaries in astronomy, astrophysics, and cosmology. With EMILIA, we have built a framework to enable multi-messenger astronomy with LISA, by developing a suit of data analysis tools based on novel techniques.