Either of two things, sounds like the first that your mac does not have Java 1.6;
http://www.gnutellaforums.com/mac-os...ck-lw-4-a.html. To check if your system has Java 1.6:
Setting up Java for Leopard (see 2nd image)
If you were previously using LW 5 & the latest Java stopped it working, solution is to use the LW beta which is stable
LimeWire 5.2.2 (Beta) - Lime Wire