The first simultaneous measurement of Hubble constant and post-Newtonian
  parameter from Time-Delay Strong Lensing
  Strong gravitational lensing has been a powerful probe of cosmological models
and gravity. To date, constraints in either domain have been obtained
separately. We propose a new methodology through which the cosmological model,
specifically the Hubble constant, and post-Newtonian parameter can be
simultaneously constrained. Using the time-delay cosmography from strong
lensing combined with the stellar kinematics of the deflector lens, we
demonstrate the Hubble constant and post-Newtonian parameter are incorporated
in two distance ratios which reflect the lensing mass and dynamical mass,
respectively. Through the reanalysis of the four publicly released lenses
distance posteriors from the H0LiCOW collaboration, the simultaneous
constraints of Hubble constant and post-Newtonian parameter are obtained. Our
results suggests no deviation from the General Relativity,
$\gamma_{\texttt{PPN}}=0.87^{+0.19}_{-0.17}$ with a Hubble constant favors the
local Universe value, $H_0=73.65^{+1.95}_{-2.26}$ km s$^{-1}$ Mpc$^{-1}$.
Finally, we forecast the robustness of gravity tests by using the time-delay
strong lensing for constraints we expect in the next few years. We find that
the joint constraint from 40 lenses are able to reach the order of $7.7\%$ for
the post-Newtonian parameter and $1.4\%$ for Hubble constant.
