I'm guessing your LaCie's SATA to USB/FireWire bridge has a proprietary password protection mechanism. Probably not full disk encryption, but just a password lock that keeps the bridge chip from allowing the drive to be mounted without successful password authentication first. Since LaCie hasn't kept their proprietary software up to date to run on modern versions of OS X, you can't tell the bridge to let your Mac mount the drive.
If you have access to a Mac that's still running an earlier version of OS X where the LaCie software works, or if you can temporarily boot your Mac from such a version of OS X (perhaps off of a USB flash drive or other external hard drive, DVD-ROM, or some other partition), then you can probably enter the password once and then disable the password protection mechanism.
After that, you should be able to use the hard drive as just a generic external hard drive on any system. You just won't be able to (nor want to) enable the password lock again.
A friend of mine had basically this same problem with a WD My Book drive, and that was the fix for him. I'll bet your LaCie situation is similar.