  We conduct the cosmological analysis by using the lens-redshift distribution
test with updated galaxy-scale strong lensing sample, where the considered
scenarios involve three typical cosmological models (i.e., $\Lambda$CDM,
$\omega$CDM and $\omega_0\omega_a$CDM models) and three typical choices (i.e.,
non-evolving, power-law and exponential forms) for the velocity-dispersion
distribution function (VDF) of lens galaxies. It shows that degeneracies
between cosmological and VDF parameters lead to the shifts of estimates on the
parameters. The limits on $\Omega_{m0}$ from the lens-redshift distribution are
consistent with those from the Pantheon+ Type Ia supernova (SN Ia) sample at
68.3% confidence level, though the uncertainties on $\Omega_{m0}$ from the
former are about 3 to 8 times larger than those from the latter. The mean
values of $\Omega_{m0}$ shift to the larger values in the power-law VDF case
and to the lower values in the exponential VDF case, compared with those
obtained in the non-evolving VDF case. In the $\omega$CDM model, the limits on
$\omega_0$, i.e. the dark energy equation of state (EoS), are consistent with
those from the Pantheon+ sample at 68.3% confidence level, but the mean values
of $\omega_0$ from the former are significantly smaller than those from the
latter. In the $\omega_0\omega_a$CDM model, the uncertainties on $\omega_0$ are
dramatically enlarged compared with those obtained in the $\omega$CDM model;
moreover, the Markov chains of $\omega_a$, i.e. the time-varying slope of EoS,
do not achieve convergence in the three VDF cases. Overall, the lens-redshift
distribution test is more effective on constraining $\Omega_{m0}$ than on the
dark energy EoS.
