You are in luck, LMS 2.5 has specific options to upgrade from an old server and migrate to a new one. You start by running the install from the new server and it will go to the old one and migrate the data. There are very detailed instructions in the documentation that comes with the upgrade CDs. Read them carefully as there are some post install scripts that you might need to run to insure that the licensing works properly.
I would however make sure you create a manual backup of the previous install and get your seed device list in the event that something goes terribly wrong.