GNOME is lauched through the gdm.service systemd service. Enable and disable it by interracting with this service.
LightDM executes *.desktop files in /usr/share/xsessions.
LightDM uses systemd to launch programs. Therefore, ~/.xinitrc is not executed. Put your user config into ~/.xprofile and the global one (i.e. keyboard layouts) in /etc/xprofile. Everything in /etc/xprofile will be available in LightDM but keep in mind that no user is logged so if you need so $HOME is not set. Also the WM is launched through /usr/share/xsessions/*.desktop so don't launch it in xprofile.
~/.xinitrc is still useful if you launch startx from a raw tty. Source your xprofiles in this file to avoid configuration repetition.