  The assumptions of large-scale homogeneity and isotropy underly the familiar
Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) metric that appears to be an
accurate description of our Universe. In this paper, we propose a new strategy
of testing the validity of the FLRW metric, based on the galactic-scale lensing
systems where strongly lensed gravitational waves and their electromagnetic
counterparts can be simultaneously detected. Each strong lensing system creates
opportunity to infer the curvature parameter of the Universe. Consequently,
combined analysis of many such systems will provide a model-independent tool to
test the validity of the FLRW metric. Our study demonstrates that the
third-generation ground based GW detectors, like the Einstein Telescope (ET)
and space-based detectors, like the Big Bang Observer (BBO), are promising
concerning determination of the curvature parameter or possible detection of
deviation from the FLRW metric. Such accurate measurements of the FLRW metric
can become a milestone in precision GW cosmology.
