  Combining the `time-delay distance' ($D_{\Delta t}$) measurements from galaxy
lenses and other distance indicators provides model-independent determinations
of the Hubble constant ($H_0$) and spatial curvature ($\Omega_{K,0}$), only
based on the validity of the Friedmann-Lema\^itre-Robertson-Walker (FLRW)
metric and geometrical optics. To take the full merit of combining $D_{\Delta
t}$ measurements in constraining $H_0$, we use gamma-ray burst (GRB) distances
to extend the redshift coverage of lensing systems much higher than that of
Type Ia Supernovae (SNe Ia) and even higher than quasars, whilst the general
cosmography with a curvature component is implemented for the GRB distance
parametrizations. Combining Lensing+GRB yields $H_0=71.5^{+4.4}_{-3.0}$~km
s$^{-1}$Mpc$^{-1}$ and $\Omega_{K,0} = -0.07^{+0.13}_{-0.06}$ (1$\sigma$). A
flat-universe prior gives slightly an improved $H_0 = 70.9^{+4.2}_{-2.9}$~km
s$^{-1}$Mpc$^{-1}$. When combining Lensing+GRB+SN Ia, the error bar $\Delta
H_0$ falls by 25\%, whereas $\Omega_{K,0}$ is not improved due to the
degeneracy between SN Ia absolute magnitude, $M_B$, and $H_0$ along with the
mismatch between the SN Ia and GRB Hubble diagrams at $z\gtrsim 1.4$. Future
increment of GRB observations can help to moderately eliminate the $M_B-H_0$
degeneracy in SN Ia distances and ameliorate the restrictions on cosmographic
parameters along with $\Omega_{K,0}$ when combining Lensing+SN Ia+GRB. We
conclude that there is no evidence of significant deviation from a (an) flat
(accelerating) universe and $H_0$ is currently determined at 3\% precision. The
measurements show great potential to arbitrate the $H_0$ tension between the
local distance ladder and cosmic microwave background measurements and provide
a relevant consistency test of the FLRW metric.
