Well...
Did you pay for it, or get the free version? If you DID pay, then, ya you can transfer it. Contact the LW (lime wire) corporation, they'll ask you some questions (ones you filled out when you registered it) answer them, then they'll give you your registration number. Step #2 remove Lime Wire from your old computer. Step #3 on your new comp, go to LW, go to DL LW, then click on something along the lines of "allready bought LW version whatever, enter information to re-install" obviously, enter your info, and yer set.

TJ

P.S. I've never done this with LW, but it's like that with all software you buy off the net.