Lacie 1T Poulton design external hard drive is clicking

Before you resort to freezers and desperation, know that the external power supplies for these things are a. crucial and b. delicate. If the output voltage is down for any reason, it can produce the same clicking symptoms. I would get to a repair shop, and ask them to test the drive with a 'known good' power supply. I did so this very morning with a LaCie drive: no more clicking, happily mounting drive...and power supply replaced under warranty. Good luck

The hard drive may have already failed by now. When a hard drive makes a clicking noise then the read/write head is flicking back and forth across the platters.
Try the external drive in another computer. If this doesn't work, try placing the LaCie in a air tight plastic bag and place it in the freezer for a hour and then connect it to a computer.
If it doesn't work then your luck has run out. There are companies that can recover data from faulty drives BUT it will cost you an arm and a leg for their services.
The reason for this high cost, they dismantle and remove the platters in the hard drive in a clean room environment and set up the platters up in jig/drive to retrieve/copy the data.