How can I administer my Lion Server from a Mountain Lion client
This seems to be an instance where Apple's push for the latest and greatest causes real world IT issues.

Per Apple's support article, HT1822 - OS X Server: Admin tools compatibility information, using Server Tools for mismatched client and server OS versions just isn't supported:


  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.


I'm not sure how useful Workgroup Manager is to you, but it may be of some value.

There's also using the command line tools over SSH, which may or may not be more desirable than Screen Sharing/Remote Desktop to you. Apple's Advanced Lion Administration guide has info on how to use the command line tools for most tasks