Back-up original images to a hard drive

Using Windows 10, can I back-up the ORIGNAL images, (not the Lr Catalog) using Lightroom Classic to an external hard drive?

Yes, of course. In fact, I consider making some sort of backups mandatotry.

However, I do not consider making manual backups using your operating system a good strategy. Backups, in my opinion, must be automated and done at regular intervals (such as daily, or weekly). Backups that rely on human interaction always are less reliable (because humans get busy, or get lazy, or just plain forget) than automated backups. So take some advice, find an automated backup program and use that.

If these back-ups can't be done within Lr, then just backing up the images normally will lose the Lr Catalog functions for those stored on the external drive?

No. Adobe is smarter than that. Your backups only need to be the original photos. Then if you need to restore the backups you can have the catalog use them instead of the originals.

Everything performed using Lightroom is stored in the catalog. That means all of the adjustments, all of the assignments to collections, everything. The images are left in their pristine state, completely untouched. The images need to be backed up once with a system of your choosing. The catalog should be backed up frequently because that is where all of your Lightroom work is stored.

LR Classic doesn't have any kind of image backup but, yes, you can backup the original images using normal backup procedures. In the future, when you import images into LRc you can also create a copy to a different location which will also create a backup.

Assuming when you say "Lr Catalog functions" you mean the develop settings, keywords, metadata, etc. that are in the catalog, that can also be backed up. One way is to use the built-in LR backup and then back up the created 'back up file' with the images. Another way is to back up the catalog file itself and its associated helper files. Keep in mind, when you do things in LRc, you are not actually changing the original files. So you should backup the catalog more often but you don't need to back up the original files just because you've changed something in LR.

Rather than answer here, I direct you to a comprehensive article on the "Backup" topic-

BACKUP - WHICH FILES?

Your original camera image files must be backed up by a method that you choose (Lightroom-Classic does not do this).

Windows users may employ something like SyncBackFree or Macrium Reflect.

Of over-riding importance is that your Catalog must always have your image files located exactly where thay are listed in the Folder panel of the Catalog.