If you have 1.9 MB more, and you do have room on that LaCie, I'd suggest downloading
Carbon Copy Cloner (donationware). It'll make an exact copy of your HD over to your LaCie, so that you can delete items from your main Mac HD to make space.
Also, running the daily, weekly, and monthly Unix cleanups manually right now would be a good idea. Open your Terminal, and enter these three commands, one at a time--hit Return after each, and wait. When the command at hand is complete, you'll receive your Terminal prompt again, just like when you started the Terminal program:
1.
periodic daily
2.
periodic weekly
3.
periodic monthly
Then simply quit Terminal. Rebooting is suggested, to help them finish--they'll remove some cruft, temporary items, etc.
You can also manually check your /tmp folder:
Finder > Go menu > Go to Folder. In the pop-up screen, type
/tmp. I'll bet it's full of older temporary files you don't need any longer.
I hope this helps!