OS X Lion Server app reinstallation on 2011 Mac Mini Server
When you boot into the recovery partition or use internet recovery - Lion will be granted as a download according to the serial number of the mac. My suspicion is server will be handled in the same manner as the OS, not as he iLife apps are granted to an Apple ID.

You will have to pay for Lion Server if you want it associated with a specific Apple ID (just like Lion) - but shouldn't have an issue when downloading to that mac.

You can test this by booting to recovery (in any of the manners) and re-installing Lion and Server to a new USB external drive.