Sorry, I don't have anything to add about Lightroom other than you might consider contacting Adobe assuming you purchased the software. They might provide some support.
As for the external drive. Not sure how it may or may not work as an external drive but if you can get it out of the case and mount it internally to a computer and run SpinRite on it (from **Home of Gibson Research Corporation** ) there's a better than even chance you can recover the drive long enough to move your LR organized files to other media. The "click of death" was actually associated with Iomega Zip Drives and that kind of behaviour in a regular hard drive usually indicates bad sectors that it cannot read - possibly in the boot sectors. SpinRite can usually correct these issues. Steve Gibson promises your money back if it doesn't work.
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