  Strongly lensed type Ia supernovae (SNe Ia) are expected to have some
advantages in measuring time delays of multiple images, and so they have a
great potential to be developed into a powerful late-universe cosmological
probe. In this paper, we simulate a sample of lensed SNe Ia with time-delay
measurements in the era of the Legacy Survey of Space and Time (LSST). Based on
the distance sum rule, we use lensed SNe Ia to implement model-independent
constraints on the Hubble constant $H_0$ and cosmic curvature parameter
$\Omega_K$ in the late universe. We find that if 20 lensed SNe Ia could be
observed, the constraint on $H_{0}$ is better than the measurement by the SH0ES
collaboration. When the event number of lensed SNe Ia increases to 100, the
constraint precision of $H_{0}$ is comparable with the result from Planck 2018
data. Considering 200 lensed SNe Ia events as the optimistic estimation, we
obtain $\Delta H_0=0.33$ $\rm km\ s^{-1}\ Mpc^{-1}$ and $\Delta\Omega_K=0.053$.
In addition, we also simulate lensed quasars in different scenarios to make a
comparison and we find that they are still a useful cosmological probe even
though the constraint precision from them is much less than that obtained from
lensed SNe Ia. In the era of LSST, the measurements of time delay from both
lensed SNe Ia and lensed quasars are expected to yield the results of $\Delta
H_0=0.26 ~\rm km\ s^{-1}\ Mpc^{-1}$ and $\Delta\Omega_K=0.044$.
