Making duplicate photo storage

One more suggestion: 

Backup your regular LR catalog to make sure there is a copy of the catalog incase the drive where your catalog resides were to fail! You can do this when quitting LR and setting up the backup location to your external drive where the photo files are stored.

Then when you clone - make a backup copy of - your external drive, you automatically also make a back up of your catalog to a second location.

To reinforce what Todd said: Do not move anything using the FInder or Explorer. Always consider Lightroom as the operating hub. You can move photos or folders onto different folders or even different drives from within the catalog. 

The best way to make a complete duplicate back up of the external drive where the Lightroom folders are located, is simply to use back up software like Carbon Copy Cloner or Super Duper however, make sure you read through every option before pressing the clone button.

If disaster stikes your regular external, you can easily "link" your LR catalog to the back up files on the second external.

Again Check LightroomQueen.com

"I updated that copy frequently. When the first external hard drive did fail however I didn't do something right because Lightroom could not read the back-up external hard drive."

How are you making these "updated copies" and using what application? Also make sure you do not move, rename, delete, or add files and folders from outside of LrC using Finder or Windows File explorer. Only perfrom these operatiosn from inside LrC using the Library module Folders panel. Performing those operations from outside LrC will cause the files and folder to show as missing. Lots of good tutorial resources here:

https://www.lightroomqueen.com/

What is the best way to make a duplicate copy of the external hard drive

There is no "best", there are many ways to do this that will meet your needs, but there are also some solutions that are clearly not "best".

In the past I've used duplicate and copying software that has put all the photos on the second drive but loses the Lightroom folder organization.

Clearly not best. Any good backup scheme will produce the exact same folder hierarchy on a different drive, and then Lightroom Classic has no particular problem using these folders on a different drive. And so something like this might meet your needs. While there are many software that will do this, I use WinZip Pro.

I suspect whatever programs you did use offer this capability (most do) and you didn't turn on that feature.

Is there a way to have a duplicate copy of my stored photos that Lightroom could read just like the original?

Explained above.

You can use any of the reputable utility applications that can make an exact copy of the storage volume containing the original photos. As an exact copy, it will have the same folder organization as the original. So if the original storage volume becomes unavailable for any reason, you just swap in the copy and have Lightroom Classic relink to the same folder structure. This is easiest if all photo folders are under a single top level parent folder, because then you only have to relink your Lightroom Classic catalog to that one folder. Lightroom Classic will then work its way down and relink all of the subfolders that match the organization in the catalog, and you'll be all set to go.

On the Mac, good backup/cloning utilities include  Carbon Copy Cloner, SuperDuper!, and Chronosync. A feature all of these have is being able to quickly update the backup to match the latest files you added (incremental backup), so that it takes just a few minutes to update your backup.

Relinking is how you would recover from something happening to the original volume. If your question is about recovering from the loss of the original photo volume, Todd is correct that you do not want to re-import (you'd lose your edits and other metadata) and you do not want to create a second catalog (again, it would not contain any of your current work on those photos).

@Chris 486 wrote:

You can duplicate the files but you will need to manage a seperate catalog file to work in your files stored in the 2nd location.

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No, that isn't necessary. If you want to catalog photos across multiple internal and external volumes, a Lightroom Classic catalog can easily do that. Each volume appears in the Folders panel as a top level listing, with its folders underneath.

What is the thing you would like to accomplish by keeping 2 sets of identical files for Lightroom to try to read?

*Edited to remove incorrect information. Thank you for the catch Conrad. Had a brain freeze there.*

What is the purpose of the duplicate copies and how will you use them. If for backup purposes they should NOT be imported back into LrC. I use FreeFileSync for keeping a duplicate backup copy of all my image files, but there are numerous other backup applications you can use for this pupose including Mac Time Machine.