You need to Copy the RAW files in their respective folders to the external drive. You need to do that manually with the File Manager program for your OS.
LR is a Non Destructive editor. It never changes the original file. It stores the edits you make in either the LR catalog file or to a XMP sidecar file or in the case of certain files to the file itself in a special area that does not change the original file depending on what options you have selected in the LR preferences and the catalog settings. In LR those edits are Applied to the original when viewing the file but if you look at the file with any other image viewing program only the original image is displayed (one exception is if you use Bridge, Photoshop and ACR and you have the edits automatically written to either a XMP file or to the file itself in certain cases). The only way to Burn In, Apply, those edits to an image is to Export it in another format, JPG or TIF.
I have no idea how you are backing up your images but there is no feature in LR to do this. It has to be done manually or with some type of backup or file syncing program. If you are using something like that it should be backing up, copying, all your images and not just JPG file.
Thank you for your quick response and information. It is helpful. The way I back up the photos is probably very basic. I export all the pictures, which includes individual folders as a catalogue from the hard to the external drive. I opened the external drive and selected one folder and the photos were in JPG format and in the original format, as shot. I'll follow your steps, below, and see what this process will provide. Thanks again.