First check the available sessions and see how they're named:
$ ls /usr/share/xsessions/ enlightenment.desktop LXDE.desktop openbox-gnome.desktop XBMC.desktop
Conveniently the prefix for the Enlightenment session is named enlightenment, imagine that. We now need to tell LightDM that we wish Enlightenment to be the default. Using your favourite editor, open up /etc/lightdm/lightdm.conf and set user-session to:
Then you need to restart LightDM:
$ sudo service lightdm restart
When LightDM restarts, you should see Enlightenment set as the default session.