Actually, this is not so simple to implement. What I did was, show what you should do: set the property and show it.
Now, it is hard to set the property when the login happens, because this code is not in naml.
You should find another place where the user properties are used. What we can do for now, in my opinion, is set this time when the user visits his own account page.
After the following line at profile_header macro:
<n.if.local_user.is_authenticated>
<then>
<n.local_user.set_property name="last_login" value="[n.now.long_format/]" />