@titan: it seems you lack the basic understanding what LXQt is and how it works - no problem, the informations are well hidden
So i will try to bring a little bit more light into: the very basic lib is libqtxdg - currently in version libqt5xdg3 3.1.0, built on that is libfm-qt3 (0.12.0) and liblxqt0 (0.12.0) - all other compontents are more or less based on these three libs. Next very important parts of LXQt are the lxqt-session and lxqt-qtplugin. First is the integrational part that deliver the session, set the used platform and start basic services. Second is a kind of glue that provide the session settings to the applications if a lxqt session is running.
And exactly there seems to be a problem, all of these components need to build against the same qtxdg and liblxqt. One can check that - if no session is present one can set the pcmanfm-qt icon theme directly in pcmanfm-qt - with a valid session running these settings are hidden.
Best bet to solve your issues is just to remove libqt5xdg* and libqt5xdgiconloader* - that will take all other LXQt components with it. After that an simple "apt install task-lxqt-desktop" will install a full LXQt with all bells and whistles - if not done yet i would suggest to remove /etc/apt/apt.conf.d/80siduction or change it to install recommends. One can purge not needed packages afterwards.
Edit: forget to mention that LXQt is strictly indipendent from any Window Manager - so on can chose every WM one like. That will work fine in theory, there might be some issues with keybindings and the way different WMs handle background applications - keybindings are handled for LXQt in lxqt-globalkeysd, so if the WM take some bindings that globalkeysd want, one should solve that in one of the settings. Second: i3 seems to mess up the classic desktop layer - so it migth be better that there is no pcmanfm-qt --desktop process running.