Adding "pam.setenv("XDG_SESSION_CLASS", "greeter");" to app.cpp, line
228, also works.
That might be better than adding "export XDG_SESSION_CLASS=greeter" to
"/etc/init.d/slim".

The decision is yours.

More info:
[gdm] pam: set XDG_SESSION_CLASS variable to "greeter" when setting up
greeter PAM session:
https://mail.gnome.org/archives/commits-list/2012-March/msg08054.html
Writing Display Managers (HOWTO):
https://www.freedesktop.org/wiki/Software/systemd/writing-display-managers/