EDIT: The below steps should not be necessary for LW versions 4.9.25 and later. LW 4.9.25 beta ships with the JavaApplicationStub from OS X 10.2.7. If you're a LW Pro user, there is also a Pro version of the beta. Of cousre, if you're reeding this a long time after this edit, the official version of LW may also be 4.9.25 or later.
/EDIT:

The problem seems to stem from LW shipping with the JavaApplicationStub from OS X 10.1. For some people, this stub causes LW to crash while creating the user's LW preferences directory.


The easiest solution is to manually replace

/Applications/LimeWire/LimeWire.app/Contents/MacOS/LimeWire

with a copy of

/System/Library/Frameworks/JavaVM.framework/Versions/Current/Resources/MacOS/JavaApplicationStub


I've edited the following instructions to use the GUI instead of the command line:

The easiest way to do this if you're not familiar with the OS X command line is the following.

(1) Go to Macintosh HD -> System -> Library -> Frameworks -> JavaVM.framework -> Versions -> Current -> Resources -> MacOS

(2) Now control-click JavaApplicationStub and select "copy 'JavaApplicationStub'".

(3) Next go to Macintosh HD -> Applications -> LimeWire

(4) Control-click on the LimeWire application and select "Show Package Contents"

(5) Go to Contents -> MacOS

(6) Control-click inside the MacOS folder and select "Paste item".

(7) Inside the MacOS folder, rename LimeWire to OldLimeWire and then rename JavaApplicationStub to LimeWire

If you're familiar with the OS X command line, this can be done in one step. However, it can be very confusing if your'e not used to the command line.