That's a kernel panic. Pretty scary. Not only is the drive at risk, but also your entire computer.
Before you do anything, I'd get a new non-Lacie drive that's large enough so that you can backup any useful files from your system disk. Backup the files from the Lacie as well. Once your computer is covered, then look at the Lacie. Is it filled to the brim? No drive should be filled up to beyond 90 per cent of its capacity.
Also, try moving the project to your internal drive, then dismount, power down and
disconnect the Lacie. Yes, with the media on it. Now open the project file from your internal drive and see if it goes through.
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