  The current gravitational-wave localization methods rely mainly on sources
with electromagnetic counterparts. Unfortunately, a binary black hole does not
emit light. Due to this, it is generally not possible to localize these objects
precisely. However, strongly lensed gravitational waves, which are forecasted
in this decade, could allow us to localize the binary by locating its lensed
host galaxy. Identifying the correct host galaxy is challenging because there
are hundreds to thousands of other lensed galaxies within the sky area spanned
by the gravitational-wave observation. However, we can constrain the lensing
galaxy's physical properties through both gravitational-wave and
electromagnetic observations. We show that these simultaneous constraints allow
one to localize quadruply lensed waves to one or at most a few galaxies with
the LIGO/Virgo/Kagra network in typical scenarios. Once we identify the host,
we can localize the binary to two sub-arcsec regions within the host galaxy.
Moreover, we demonstrate how to use the system to measure the Hubble constant
as a proof-of-principle application.
