I am running exactly the same (LimeWire Pro on a PowerBook G3 with 9.2.1) but do not have problems. After highlighting the download item in the downloads window in Search, the launch button becomes active and when clicked it Launches iTunes application, moves the mp3 into the Song list and starts playing the music!
Are you remembering to highlight the download item to activate the Launch button??
Also, try looking at the answer to the previous question 'Transfering music files LW to iTunes'