Mac external drive, file rights
In the Finder, get info on the volume (under the File menu). First, check the General section of the info window to make sure it's in one of the Mac OS Extended formats (probably "Mac OS X Extended (Journaled)"); if not, you'll need to reformat it. I'm not familiar with the Lacie setup program, but you can use Disk Utility to do this.

If it's in Mac OS X Extended format (or a variant), expand the Sharing &amp; Permissions section of the info window, and see if it has an "Ignore ownership and permissions" option at the very bottom. If it's there and enabled, click the padlock and authenticate as an administrator, then disable the "Ignore..." option.

Explanation: when OS X sees a new external volume, it assumes it's either come from another computer, going to another computer, or both.  Since there's no general correspondence between accounts on different computers, OS X figures there's no point in trying to track file ownership and simply disables it. If you enable ownership in the Info window, OS X will start storing &amp; respecting ownership on files on that volume.