Please read the instructions carefully. There are two steps in this process:
1: Restoring the image from a Time Machine backup. That has nothing to do with Lightroom, so you can turn it off (but there is no harm in leaving it running in the background either). Time Machine doesn't 'find the folder for you', you have to tell Time Machine where the image was. If you don't know that, it may become a matter of trying folder after folder until you found it. I'm typing this on my iPad so I can't post some screenshots to make it easier to understand, so read this:
How to view and restore specific files using Time Machine
2: Once the image is restored, you
know where it is. So it won't be a matter of ctrl-clicking on the folder in Lightroom where you '
think' the image was, it will be ctlr-clicking on the folder you
know you just restored the image to. Or importing the image from where you know you restored the image to (like the desktop). There isn't really much difference between 'synchronize folder' and 'import'. In both cases you import the image into Lightroom. If you feel more comfortable using the standard import method, then just use that one.
P.S. If your catalog is on an external hard drive and your images are on yet another hard drive, then I do hope that you actually have a Time Machine backup that covers all those drives. Time Machine can backup multiple drives, but always to a single destination drive so that drive must be quite large if it does indeed contain a backup of three source drives...