In $\sim 2034$ the Laser Interferometer Space Antenna (LISA) will detect the coalescence of massive black hole binaries (MBHBs) from $10^5$ to $10^7$ solar mass up to $z\sim 20$. The gravitational wave (GWs) signal is expected to be accompanied by a powerful electromagnetic (EM) counterpart, from radio to X-ray, generated by the gas accreting on the binary.If LISA locates the MBHB merger within an error box $< 10 \, \rm deg^2$, EM telescopes can be pointed to detect the emission from the last stages of the inspiral or the very onset of the nuclear activity, paving the way to test the nature of gas in a rapidly changing space-time. Moreover, an EM counterpart will lead to exquisite tests on the expansion of the Universe as well as on the velocity propagation of GWs. In this talk, I present the new forecasts on the number of EM counterparts that we expect to detect over the LISA mission (Phys.Rev.D106, 103017). Starting from a population of MBHB binaries, we compute the expected EM emission under different assumptions. We find that, in the best case scenario, we expect between 7 and 20 EM counterparts in 4 yr of LISA mission. However these numbers reduce to 2-3 EMcps in 4 yr if we include obscuration and collimated radio emission. Moreover the typical galaxies hosting the GW event are faint and challenge the capabilities of future EM telescopes.