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Gravitational lensing of gravitational waves (GWs) is a powerful probe of thematter distribution in the universe. Here we revisit the wave-optics effectsinduced by dark matter (DM) halos on the GW signals of merging massive blackhole binaries (MBHBs), and we study the possibility of discerning these effectsusing the Laser Interferometer Space Antenna (LISA). In particular, we includethe halos in the low-mass range of $\rm 10^5-10^8\, M_\odot$ since they are themost numerous according to the cold DM model. We simulate the lensed signalscorresponding to a wide range of impact parameters, and we find distinguishabledeviation from the standard best-fit GW templates even when the impactparameter is as large $y\simeq50$. Consequently, we estimate that over$(0.1-1.6)\%$ of the MBHBs in the mass range of $\rm 10^{5.0}-10^{6.5}\,M_\odot$ and the redshift range of $4-10$ should show detectable wave-opticseffects. This probability is one order of magnitude higher than that derived inprevious works. The uncertainty comes mainly from the mass function of the DMhalos. Not detecting any signal during the LISA mission would imply that DMhalos with $\rm 10^5-10^8\, M_\odot$ are less numerous than what the cold DMmodel predicts.

A Higher Probability of Detecting Lensed Supermassive Black Hole Binaries by LISA