A few simple things to try and eliminate the problem in this order:

1) Run all tasks from MacJanitor 1.3 (Panther version) (http://personalpages.tds.net/~brian_hill/downloads.html)
2) Repair disk permissions from Disk Utility
3) Remove the Limewire app from Dock (drag away and let go!)
4) Do a search in Finder for all entries 'Limewire' and delete all those entries EXCEPT the 'application' called 'Limewire' (should be a lovely lime icon next to it). Deleting all the other entries will not cause any problems but you may have to set up your Limewire preferences again - no big thing.
4) Go back to your Applications folder and execute the Limewire app. If this works (all obvious basics are covered) drag that working Limewire app into your dock.