Contrary to what the Apple Enterprise support representative told me yesterday you can’t manage a Lion Server remotely from Mountain Lion. Since the Lion Server app will not work on Mountain Lion, I was told that if I purchased Mountain Lion Server on my MacBook Pro that it would work with Lion Server. This is not the case, when opening the Server app and connecting to a Lion Server you get this message:
Server requires OS X 10.8
The server you’re trying to connect to is not running OS X 10.8. Install OS X 10.8 on the server and try again.
It does however give you the option to “launch screen sharing session” which will let you connect to the Lion Server.
I also have found a support article since then that idicates the same thing: http://support.apple.com/kb/HT1822
So if you rely on the Server app or Server Admin app to manage your server you might want to think twice about updating to Mountain Lion if you are still running a Lion Server. Or do what I did and at least have a virtual machine of Lion as a backup.