LrC doesn't recognize one external HD

. I have all my photos on an external HD along with a backup of my LR 6 catalog. 

After you fix your problem, I would recommend you take care of a future problem. Backups should be on a separate hard drive, separate from the original, now your catalog backup is apparently on a different hard drive than the originals catalog, BUT on the same hard drive containing your original photos? The photos need to be not on the same hard drive as the backups, oh they need to be backed up, but keep originals and bah kudos separate.

At what moment does Lightroom not 'recognise' the HD? Lightroom is not a file browser. In the folder panel it only shows you drives that contain at least one photo that has been imported in the catalog. If there are no such photos on a particular drive, then Lightroom will not show this drive in the folder panel. It will show it in the Import dialog (so you can import photos from it or copy/move imported photos to it).

I have checked 3 times -- LR has full-disk access in System preferences>security & privacy.  I read the previous post and followed its suggestions.  Didn't solve the problem. Why would LR recognize one external HD and not another?

As a first basic step, I would be sure that LR has full-disk access in System Preferences > Security & Privacy.  See here for details (taken from another post) :

https://community.adobe.com/t5/lightroom-classic-discussions/lightroom-catalog-cannot-be-used-becaus...

Best regards