  The gravitational waves (GW) emitted during the coalescence of supermassive
black holes (SMBHs) in the mass range 10^4-10^7 M_sun will be detectable out to
high redshifts with LISA. We calculate the size and orientation of the
three-dimensional error ellipse in solid angle and redshift within which the
LISA event could be localized using the GW signatures alone. We take into
account uncertainties in LISA's measurements of the luminosity distance and
direction to the source, in the background cosmology, in weak gravitational
lensing magnification due to inhomogeneities along the line of sight, and
potential source peculiar velocities. We find that weak lensing errors exceed
other sources of uncertainties by nearly an order of magnitude. Under the
plausible assumption that BH mergers are accompanied by gas accretion leading
to Eddington-limited quasar activity, we then compute the number of quasars
that would be found in a typical LISA error volume, as a function of BH mass
and redshift. We find that low redshifts offer the best opportunities to
identify quasar counterparts to cosmological standard sirens, and that the LISA
error volume will typically contain a single near-Eddington quasar at z=1. This
will allow a straightforward test of the hypothesis that BH mergers are
accompanied by bright quasar activity and, if the hypothesis proves correct,
will guarantee the identification of a unique quasar counterpart. This would
yield unprecedented tests of the physics of SMBH accretion, and offer an
alternative method to precisely constrain cosmological parameters [abridged].
