Make sure you have the "auto" option in your /etc/fstab file on the line that specifies your LaCie drive. The "defaults" option should include the auto option within it, but there's no harm in forcing automatic mounting at boot by explicitly declaring the "auto" option.
Access your fstab file with an editor of your choice (e.g.: vi, nano, etc.). I prefer vi, so...
Now add a line of code for your drive. I'll assume it's formatted as ntfs but if it isn't, you'll need to make some changes to the following example:
This addition to your /etc/fstab should mount the drive during boot providing you have already created the directory: /media/LaCie
/dev/sdc1 /media/LaCie ntfs auto,defaults 0 0
The man page for fstab (at least in Ubuntu) is pretty good:
If you wanted to un-mount it after boot:
Conversely, if you wanted to re-mount it after you had un-mounted it:
sudo umount /media/LaCie
sudo umount /dev/sdc1
sudo mount /media/LaCie
sudo mount /dev/sdc1