Can I install a Lacie 4TB (Seagate-) SATA drive in my early 2008 MacPro

There are no known issues installing such a drive. The screws should even fit oK.

Later large drives such as 6GB have some models where the mounting screws closest to the platters have their screw-penetration depth limited, and even more recent large drives may have the screws nearest the platters relocated so that they no longer line up with the screws on the sled.

For models that don't line up, you need to go back to fundamentals: the purpose of the sled screws is to hold the drive fairly level as it slides in so that the connector at the back will mate properly. ANY way you can accomplish that (and still be able to slide the drive in and out) means the drive will work fine.

There are some 6GB and larger models that do not spin up properly after a restart, but work fine after a Shutdown/Restart.

The effective maximum storage size allowed is literally millions of times larger than any drive you can buy today, as long as you are running 10.4 or later.

LaCie had some problems some years ago with their external drives. The power supplies tended to fail. I think in general it is far better to buy a decent enclosure and install whatever drives one prefers. The cheap externals from Seagate and WD and others use the cheapest enclosures they can get away with, and they are often difficult to pry open if you need to extract the drive for trouble shooting.

Data Rescue (the most recent version is 5) might be able to recover files from the 4TB drive.