  The luminosity distance is a key observable of gravitational-wave (GW)
observations. We demonstrate how one can correctly retrieve the luminosity
distance of compact binary coalescences (CBCs) if the GW signal is strongly
lensed. We perform a proof-of-concept parameter estimation for the luminosity
distance supposing (i) strong lensing produces two lensed GW signals emitted
from a CBC, (ii) the Advanced LIGO-Virgo network detects both lensed signals as
independent events, and (iii) the two events are identified as strongly lensed
signals originated from the same source. Taking into account the maximum
magnification allowed in two lensing scenarios and simulated GW signals emitted
from four different binary black holes, we find that the strong lensing can
improve the precision of the distance estimation of a CBC by up to a factor of
a few compared to that can be expected without lensing.
