@hmollercl brought up some interesting quirks about lxqt-sudo and after doing some hunting I found a really new patch which is actually really old (first commit in 2016) but it strips out all but the X and locale environment variables so that we don't end up with file permissions changing and the like. This is probably something we want to get in right away, but perhaps a release is on the horizon?
P.S. Contrary to what @tsimonq2 said, lxqt-sudo is a front end to sudo or su and is in no way related to pkexec. Furthermore, pkexec (according to its manpage) is not designed for GUI apps for security reasons.