Are you trying to write to the same disc your reading from to do the FCP output? If so, that might not be the best idea. It makes sense to render to your system disc and copy it over later. Besides, it’s a good idea to keep your project files on a seperate disc anyway.
Also, I have better luck with compositing in FCP if I just bring the livetype project into FCP and render it w/ everything else. It can be a hassle when you constantly have to reconnect the media, but it renders everything at the same time (no double-step renders)- a bit slower but handy from a workflow standpoint.