  The mass and distance of a binary black hole (BBH) are fundamental parameters
to measure in gravitational-wave (GW) astronomy. It is well-known that the
measurement is affected by cosmological redshift, and recent works also showed
that Doppler and gravitational redshifts could further affect the result if the
BBH coalesces close to a supermassive black hole (SMBH). Here we consider the
additional lensing effect induced by the nearby SMBH on the measurement. We
compute the null geodesics originating within $10$ gravitational radii of a
Kerr SMBH to determine the redshift and magnification of the GWs emitted by the
BBH. We find a positive correlation between redshift and demagnification, which
results in a positive correlation between the mass and distance of the BBH in
the detector frame. More importantly, we find a higher probability for the
signal to appear redshifted and demagnified to a distant observer, rather than
blueshifted and magnified. Based on these results, we show that a binary at a
cosmological redshift of $z_{\rm cos}=(10^{-2}-10^{-1})$ and composed of BHs of
$(10-20)M_\odot$ could masquerade as a BBH at a redshift of $z_{\rm cos}\sim1$
and containing BHs as large as $(44-110)M_\odot$. In the case of extreme
demagnification, we also find that the same BBH could appear to be at $z_{\rm
cos}>10$ and contain subsolar-mass BHs. Such an effect, if not accounted for,
could bias our understanding of the origin of the BHs detected via GWs.
