Dave
Though I have not tried it you may be able to install / configure xinit-xsession so that you can load ~/.xinitrc from lightdm. Then you can symlink (or call in) /usr/local/bin/desktop-session with ~/.xinitrc. This should then work similar to slim by running desktop-session (to build the particular session) though you cannot choose which session directly from lightdm. Instead desktop-session will load the default session which is the last one used. Therefore to change to another session you would use the “desktop” menu under the root menu. If that works then you should specify xinit-xsession as the default in /etc/lightdm/lightdm.conf
Wow that is a lot of “sessions”.
No idea if this will actually work, you will need to try. It is kind of ass/u/me.d that if you are using another login manager you know what you need to adapt. Generally a different desktop environment is used…
Computers are like air conditioners. They work fine until you start opening Windows. ~Author Unknown