Strangely enough, i also have a LaCie drive, but dont use it to back up, i use it as my iTunes Media Folder (4 TB). Sometimes i notice it starts up for no reason even when iTunes is off, and i notice my Mac seems slower, so i eject the drive. However, after ejecting, the drive restarts itself and tries to reinvade my work environment. I then just pull the plug on it in anger. I am not sure if there is perhaps a virus on it trying to upload stuff to the internet or what, but doubt it, as have read many similar complaints from LaCie owners. I used to think LaCie were good, but after reading a lot, it seems they have a slightly different way of working to other drives, and a lot of people have this or similar problems.
Try changing your brand of hard drive. I have two wd my passport drives and a samsung drive which all are fine and do not produce this problem. Recommend doing away with LaCie, and doing away with the belief that they are good products.
I would like to take this opportunity to thank Apple for changing the style of thesesupport forums, to allow people to express their opinions. In past years, this was not possible and the forums were highly moderated, deleting people's posts if any criticism of Apple was evident. These days, Apple has placed a disclaimer in the footer of the forums and let people a bit more freedom of expression. Thank you Apple., its the right thing to do, and creates less antimony towards the company itself. I appreciate it, and im sure a lot of other people do too. It used to be like a concentration camp, now its a more useful place to come to.