  We proposed a model-independent method to constrain the cosmological
parameters using the Distance Sum Rule of the FLRW metric by combining the time
delay distances and the comoving distances through a multi-messenger approach.
The time delay distances are measured from lensed gravitational wave~(GW)
signals together with their corresponding electromagnetic wave~(EM)
counterpart, while the comoving distances are obtained from a parametrized
fitting approach with independent supernova observations. With a series of
simulations based on Einstein Telescope, Large Synoptic Survey Telescope and
The Dark Energy Survey, we find that only 10 lensed GW+EM systems can achieve
the constraining power comparable to and even stronger than 300 lensed quasar
systems due to more precise time delay from lensed GW signals. Specifically,
the cosmological parameters can be constrained to ~$k=0.01_{-0.05}^{+0.05}$ and
~$H_0=69.7_{-0.35}^{+0.35}$ (1$\sigma$). Our results show that more precise
time delay measurements could provide more stringent cosmological parameter
values, and lensed GW+EM systems therefore can be applied as a powerful tool in
the future precision cosmology.
