New comment by Hoshpak on void-packages repository

https://github.com/void-linux/void-packages/issues/13326#issuecomment-515651652
Comment:
So it seems that lxdm ist the culprit here. If I start lxqt via xinitrc without a display manager, I have only one ConsoleKit session and the shutdown and reboot buttons work. lxdm establishes two sessions, one of which is a login session and the buttons do not work.

It could also been a compatibility issue between lxdm and any of the components involved since the buttons worked in the current lxqt live image which is from 2018. However since lxdm is unmaintained for four years now, chances that someone is going to fix it are virtually nonexistant. I can only recommend switching to another DM at this point, I briefly tried lightdm and it seems to establish the ConsoleKit session properly.