Strong-lensing rates of massive black hole binaries in LISA

Similarly to electromagnetic (EM) signals, gravitational lensing by intervening galaxies can also affect gravitational waves (GWs). In this paper, we estimate the strong-lensing rate of massive black hole mergers observed with LISA. Given the uncertainties in the source populations as well as in the population of galaxies at high redshift, we consider: six different source population models, including light and heavy seeds, as well as three lens population models, including redshift-independent and redshift-dependent evolution properties. Among all the scenarios explored, the expected number of strong lensed events detected in a 4-year observation time in LISA ranges between 0.13-231 with most of them having two (one) images detectable in the heavy (light) seed scenarios. The event numbers obtained correspond to 0.2%--0.9% of all detected unlensed events. Out of all the detectable strong-lensed events, up to 61% (in the light-seed scenario) and 1% (in the heavy-seed scenario) of them are above the detectability threshold solely due to strong lensing effects and would otherwise be undetectable. For detectable pairs of strong-lensed events by galaxy lenses, we also find between 72%--81% of them to have time delays from 1 week to 1 year.