I couldn't check on that before as I was pretty sure you were not using lxdm which I am using on the external 64OB install and that install is OB only.
But I am now on the internal Stoned Lizard where I use lightdm and have both Xfce and OB installed. I even logged out to double check that the option for what DE you log into is still there.
It is there on this install and appears to work. didn't change over to OB but it has always worked in the past.
There should be 3 options on the top panel of lightdm and the one 3rd from the right should give you that option.
I also checked in
and see nothing in either of them that should need changed to have that option. Mine are all dead default settings except for
on which I have modified the background to use a different image.
I think that while those files are all pretty long (except user.conf) that there are only about 3 lines each not commented out.
I would check that panel again to make sure you are correct in your description of the problem and if so I would take these steps in trying to correct the problem.
# dpkg-reconfigure lightdm
Reboot and check. If that hasn't fixed it then
# apt-get purge lightdm
# apt-get install lightdm
You could try
# apt-get install --reinstall lightdm
instead of the first (dpkg) option but the dpkg command has had a better history with me in correcting slightly screwed applications.
As long as you lightdm package isn't in and of itself somehow screwed all it needs is the install scripts rerun and dpkg will do that. If the package is screwed the install -- reinstall will end up pretty much just running like a package upgrade and that may not change any files at all whereas if you purge the package before reinstalling it all the system config files will be removed and you get a new, clean start.
If you have changed anything in the "greeter" you may want to save that file someplace to see what you did. I wouldn't use that file as a replacement because there may be something in it causing the problem. But you would have the relevant line(s) you modified as a guide to what to do with the new one. If this is the case make sure you back up the original file before modification.
Edit: code tags... <sigh>