try lookinig at the site of MacroMedia, the makers of FLexLM
http://www.macrovision.com/services/support/flexlm/lmgrd.shtml
If your OS is not listed there, then i sould stay on Windows.
If it is there, i think the network licecnse will run on the machine (re-author code as you got a new IP adress and host name), but i suppose anything special (Lic borrowing, redundant servers, Report tools, ) will be an adventure to test and set up !