A Higher Probability of Detecting Lensed Supermassive Black Hole
  Binaries by LISA
  Gravitational lensing of gravitational waves (GWs) is a powerful probe of the
matter distribution in the universe. Here we revisit the wave-optics effects
induced by dark matter (DM) halos on the GW signals of merging massive black
hole binaries (MBHBs), and we study the possibility of discerning these effects
using the Laser Interferometer Space Antenna (LISA). In particular, we include
the halos in the low-mass range of $\rm 10^5-10^8\, M_\odot$ since they are the
most numerous according to the cold DM model. We simulate the lensed signals
corresponding to a wide range of impact parameters, and we find distinguishable
deviation from the standard best-fit GW templates even when the impact
parameter 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-optics
effects. This probability is one order of magnitude higher than that derived in
previous works. The uncertainty comes mainly from the mass function of the DM
halos. Not detecting any signal during the LISA mission would imply that DM
halos with $\rm 10^5-10^8\, M_\odot$ are less numerous than what the cold DM
model predicts.
