Laser Interferometer Space Antenna (LISA) will extend the search for gravitational waves (GWs) at |$0.1\, {-}\, 100$| mHz where loud signals from coalescing binary black holes of |$10^4 \, {-}\, 10^7\, \, \rm {M}_{\odot }$| are expected. Depending on their mass and luminosity distance, the uncertainty in the LISA sky-localization decreases from hundreds of deg2 during the inspiral phase to fractions of a deg2 after the merger. By using the semi-analytical model L-Galaxies applied to the Millennium-I merger trees, we generate a simulated universe to identify the hosts of |$z\, {\le }\, 3$| coalescing binaries with total mass of |$3\, {\times }\, 10^{5}$| , |$3\, {\times }\, 10^6$| , and |$3\, {\times }\, 10^7\, \rm {M}_{\odot }$| , and varying mass ratio. We find that, even at the time of merger, the number of galaxies around the LISA sources is too large (|${\gtrsim }\, 10^2$|) to allow direct host identification. However, if an X-ray counterpart is associated to the GW sources at |$z\, {< }\, 1$| , all LISA fields at merger are populated by |${\lesssim }\, 10$| active galactic nuclei (AGNs) emitting above |${\sim }\, 10^{-17} \, \rm erg\, cm^{-2}\, s^{-1}$|. For sources at higher redshifts, the poorer sky-localization causes this number to increase up to |${\sim }\, 10^3$|. Archival data from eRosita will allow discarding |${\sim }\, 10{{\ \rm per\ cent}}$| of these AGNs, being too shallow to detect the dim X-ray luminosity of the GW sources. Inspiralling binaries in an active phase with masses |${\lesssim }\, 10^6\, \rm {M}_{\odot }$| at |$z\, {\le }\, 0.3$| can be detected, as early as 10 h before the merger, by future X-ray observatories in less than a few minutes. For these systems, |${\lesssim }\, 10$| AGNs are within the LISA sky-localization area. Finally, the LISA-Taiji network would guarantee the identification of an X-ray counterpart 10 h before merger for all binaries at |$z\, {\lesssim }\, 1$|. [ABSTRACT FROM AUTHOR]