Well, I’m no Ubuntu guru, but I think this is your problem. You need to restore your original config file, whether that means manually deleting it or regenerating lightdm’s configuration like ouromov suggests (actually, that sounds like the better option). Perhaps his command failed because you were not in read-write mode.
Unfortunately (or rather fortunately?) I’ve never used Ubuntu’s recovery mode so I can’t help much here. This is about the time I’d be checking the documentation: https://wiki.ubuntu.com/RecoveryMode
This states the root partition is mounted read-only by default, this is probably your problem. I’d follow these instructions to get into read-write mode, then try running the commands ouroumov suggested again.
If you end up having to reinstall and you haven’t backed up your files before, you may still be able to save your files. Even with your installation borked, you can still boot up an UM live USB (like you used to install with). You can back up your files and reinstall from the live CD.
First boot the live CD, then back up your files. Click “try Mate”, open up the file manager, and access the files on your system drive. From here you can attack some kind of external storage and back up everything important.
Then you can try reinstalling UM without losing your home folder. Follow these instructions: https://help.ubuntu.com/community/UbuntuReinstallation Basically click through the prompts as normal until you reach the “Installation type” menu, then select “Reinstall” or “Upgrade” (the options available will depend on whether the live CD is a newer version of UM or the same as the system you are trying to rescue). Basically it reinstalls or upgrades your system in place, trying to preserve your home folder. You should still back up your important stuff first.
If that still doesn’t work, then reinstall again, this time selecting “erase and reinstall”. At least you’ll still have your files!