Can't use my Lightscribe Drive or software to write on the Disc

No not even Roxio Toast will do it. Lightscribe was a technology used by HP to burn custom labels into the top of CDs & DVDs, it required lightscribe media and if memory serves me it was only monochromatic. It was designed to replace paper labels that were commonly put on media but I don't think it ever really took off. I worked for HP from 2002 to 2009 and recall it from that time frame.

There really is no need to use that type of software - an external drive does not need any to function. If you simply want to drag and drop, you can do that. If you want a continuous backup, use Time Machine (you already have it), or, if you want a bootable clone, use either SuperDuper or CarbonCopyCloner.

FYI, when you get a new hard drive, you should erase and format it for Mac before using it. Now, if you are not able to access your files because the software no longer works, you will need to either revert to a previous OS (only possible if you erase your drive and have a full backup) or need to abandon them by erasing the external, making sure it is formatted correctly, and then starting with one of the methods outined above.

Lightscribe isn't used for recording data on CDs and DVDs. Nearly 20 years ago HP invented a process that lets the laser of an optical drive print directly on an optical disc, eliminating the need for paper labels. My lightscribe drive died around the time of Mac OS 10.11 so I'm amazed it was working as of Mojave. I'm sure the software was 32 bit.

Got it in one. It was monochromatic and required media that as about 25% more expensive than regular. But since paper labels and Apple's slot loading drivers were recipe for disaster, they were handy. HP did a lousy job of marketing it and I think that at first they charged a royalty to software developers who wanted to incorporate the printing tech into their software. I had several programs that could print optical disc labels but found only 1 (other than HP's weak program) that could print.

Check with the developers fo the Lightscribe software to see if they have updated the software to be compatible with Catalina.

Well if it's not a 64 bit app then you will need to search for a replacement app if one exists.

Good luck.

ahh, thanks; I assumed it was an app for moving data (much like the stuff that is on WD drives).

So, if it is for burning media, then the OP will need something like Roxio Toast.

Okay, I finally got it (LOL),

My very old version of Toast has an extra feature to print labels (I've never used it); checked their website and the latest version does not seem to have that.

No worries, Lightscribe was HP's Ford Edsel.