A few things to try:
Remove the LaCie drive entirely, try recording to the system drive first and see if the problem persists. If it does change out your Thunderbolt cables for Apple Thunderbolt cables.
Consider creating a separate partition on your drive and install a fresh version of OS, install only the apps you need to do your recording and test to see if that resolves it.
If it does, re-introduce the LaCie drive back into the system and see if issue arises, then you'll know. If the drive is more than a certain percentage full, 75% or so, it may be pulling more voltage than the power supply for the drive can handle. Try using a fresh clean drive that has less than 25% of storage or nothing on it.
If you're still having issues, contact support and/or go to your Apple store to see if they have any suggestions.
That should do it.