I recently installed Debian9 (netinstall) and installed LXDE desktop after that. I found lightdm is installed as login manager. I installed lxdm and used following command to purge lightdm:

I found that it removed all of following packages!

Why does removing lightdm remove so many packages? All these do not seem to be its dependencies since it is supposed to be a "light" display manager.

Also, although the system seems to be working all right (including printer and scanner), will any major applications be affected by above step?

Those look to me like dependencies of dependencies and recommends. It should not affect anything, though I do not like that it removes xinit, but if all works for you after that, you are fine. Did you try to reboot after that and see what happens?

System works okay even after reboot.

Even xorg, xsane, x11-apps and x11-session-utils have been removed.

Is this grouping set up by Debian Linux or by 'lightdm' package or by LXDE desktop?

Package maintainers are part of the Debian Linux. So, it is both by Debian and package maintainer of lightdm package. Which was, I guess, pulled in as recommended package for lxde.