Lacie External Hardrive doesn't show up on Mac or in Disk utility
Spinning disk drives fail, and its clicking-then-silence and invisibility to the host computers both indicate that this one has given up the ghost. 

Expensive disk-repair software such as DiskWarrior might be able to repair it, or to retrieve the data. Given the clicking noise followed by silence, however, this is very unlikely. I wouldn't expect DiskWarrior to be successful.

Hard drives aren't repairable. The data can be retrieved by specialist businesses, but at significant cost.