Ken --
I found it easier to go with the GUI method rather than the command line route. One little typo & you'd get the "no such file/directory" error.
Summarizing/restating kmag's solution:

From the "Macintosh HD" icon on the desktop, navigate down into System -> Library -> Frameworks -> JavaVM.framework -> Versions -> Current -> Resources -> MacOS. Whew!!
Then COPY the "JavaApplicationStub" file.
Next go to Macintosh HD -> Applications -> LimeWire, and <Ctrl>-click on the LimeWire icon. Select "Show Package Contents" from the menu that pops up. In the window that pops up, go into the Contents folder, then into the MacOS folder.
Now PASTE the "JavaApplicationStub" file in here.
Finally, RENAME the file "LimeWire" to something else (e.g. "OldLimeWire"), and RENAME "JavaApplicationStub" to "LimeWire".

Hope this didn't confuse things more. Thanks again to kmag!