This is a common problem if you have incorrectly edited some of the configs for lightdm, or one of the available greeters.
As far as I understand things, the lightdm greeters are basically standalone programs/scripts that hook into the lightdm API. Some greeters support themes, others do not.
Which lightdm greeter are you actually using at the moment? And what changes have you made to its configs?
If memory serves, I'm currently using the lightdm-kde-greeter, but I've set a custom theme for it. It was quite a while ago since I set it up, so I can't remember but I THINK I set the theme from inside KDE's settings manager. I don't think I manually edited any of the configs.
In Debian, there is a separate package for the lightdm-gtk-greeter, called lightdm-gtk-greeter-settings, which I think contains the tool/s to allow you to change the appearance/theme of the gtk greeter. So if you are using the gtk greeter - you might want to install and use that package.
In order to get lightdm working properly again, I'm guessing you'd probably need to do a forced re-install and re-configure of lightdm and/or the required lightdm greeter. Once you have lightdm working properly again, you can then take a look at changing the look/feel/theme of the greeter using the appropriate tools.