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:

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.