I'm no one to give advice here, but if this would happen to me, I don' think it wouldn't hurt to first remove LightDM and then install back LightDM. You have nothing to lose and problem may go away.
Another option would be to first remove LightDM and then install different. I know on Xfce you can LightDM replace with MDM (Mint DM), not sure about Budgie and Gnome
To install LightDM:
sudo pacman -Sy lightdm lightdm-gtk-greeter
Did you report the problem in the last stable update?