  Although the cosmic curvature has been tightly constrained in the standard
cosmological model using observations of cosmic microwave background
anisotropies, it is still of great importance to independently measure this key
parameter using only late-universe observations in a cosmological
model-independent way. The distance sum rule in strong gravitational lensing
(SGL) provides such a way, provided that the three distances in the sum rule
can be calibrated by other observations. In this paper, we propose that
gravitational waves (GWs) can be used to provide the distance calibration in
the SGL method, which can avoid the dependence on distance ladder and cover a
wider redshift range. Using the simulated GW standard siren observation by the
Einstein Telescope as an example, we show that this scheme is feasible and
advantageous. We find that $\Delta\Omega_k\simeq 0.17$ with the current SGL
data, which is slightly more precise than the case of using SN to calibrate.
Furthermore, we consider the forthcoming LSST survey that is expected to
observe many SGL systems, and we find that about $10^4$ SGL data could provide
the precise measurement of $\Delta\Omega_k\simeq 10^{-2}$ with the help of GWs.
In addition, our results confirm that this method of constraining $\Omega_k$ is
strongly dependent on lens models. However, obtaining a more accurate
phenomenological model for lens galaxies is highly predictable as future
massive surveys observe more and more SGL samples, which will significantly
improve the constraint of cosmic curvature.
