Copy a *.jpg (preferably a size of your screen's native resolution, DO NOT use another file type, the greeter has issues with other file types, like not being able to read them) to:
/usr/share/pixmaps
(this directory is readable by LightDM greeter to display a pic as a background, it has permissions issues with other directories on boot), copy the directory and filename to lightdm-gtk-greeter.conf in /etc/lightdm, specifically the "background=" line, example:
background=/usr/share/pixmaps/BabyDuckPaddling1920x1080.jpg
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