OSX Mavericks and OSX Lion Login Server

Updating Server.app is not really necessary. OS X Mavericks clients are backward compatible with OS X Lion Server, in the same way Mavericks Server is backward compatible with Lion clients. It is only required to update Server.app if you want the new features available in the updated OS X Server, or if you wish to upgrade the host OS on the server (i.e. Lion Server.app is not compatible with OS X Mavericks).

Are you asking if your workstation (client) iMac can be upgraded to Mavericks and still retain the functionality of accessing your user account / files / etc provided by the Lion Server?

If so then yes. The only functionality that the central Lion Server couldn't provide to you is the Software Update Server, where software updates are cached by and served out from your office's server. In order to retain the Software Update Server, and possible Caching server, functionality you would need to update the Lion Server to Mavericks.

Aside from that you should still be able to access your network user account, shared files, etc from the Lion Server using your iMac running Mavericks.

Source: I currently have 9 Mavericks clients accessing our central Mac Pro running Mountain Lion server. Software Update Server is the only function of the server that doesn't work with the Mavericks clients. For software updates I upgraded an old secondary Mac mini server to Mavericks and installed the 3.0 Server client, the only service that is active is Software Update Server and only the Mavericks clients pull from it.