Interesting. If I install LXQT from Ubuntu without LXQT (with apt with/without --no-install-recommends or with tasksel) or even from Ubuntu mini ISO (with tasksel), then keyboard layouts configured in LXQT automatically, also keyboard layouts work normally on sddm login screen.
I comare ~/.config dir on both systems, and there are no something lxqt related difference .Only on system, installed from Lubuntu ISO (the “first” system), there was no ~/.config/lxqt/lxqt-config-locales.conf files [contained only string with __userfile__ = true], but even with this file changing keyboard layouts still not working on the “first” system. Packages files of sddm, sddm-lubuntu-theme are same on both systems.
So, it’s needed some another comparing…