I have downloaded the server app for 10.7.5 but I can not install it on my 10.8 MacBook Pro. Can this be done?
According to the Apple Web site:
To administer Lion Server, use Server app and the Server Admin Tools 10.7 on OS X Lion. The Server Admin Tools 10.7 are are available from Apple Support Downloads.
To administer Lion Server from a client with a different version of OS X, connect to the server using Screen Sharing or Apple Remote Desktop. You can also use Workgroup Manager 10.8 on Mountain Lion to connect to Lion Server.
One alternative to what Apple suggests is to run a VM of whatever OS you need to use to do remote management. This is what I do on my laptop with Lion. I don't have the same luxury with Snow Leopard, although I guess I could virtualize an instance of it, and run it on the desktop side as well.
You might try redownloading it from the Mac App store - Server
Since the version of Server changed between 10.7 & 10.8 you won't be able to install it using the same package as you did for the server but if you can redownload it from the Mac App store I believe you should be able to connect it to your 10.7 server. I'm currently running 10.8 server on our Mac Pro server and using Server beta on my 10.9 MacBook Air to administer it. It seems like I was in a setup similar to yours this time last year.
Once you launch the Server app you can connect to the 10.7 server by choosing "Other Mac" from the main window (see attached image), enter the server address/name along with your server admin credentials.
Hopefully this works for you!