Why is my MacBook continuously ejecting Western Digital external hard drive?

I've heard of problems like this too and they are unlikely to have anything to do with Lightroom, more likely a problem with macOS that requires troubleshooting. The advice earlier to set Energy Saver preferences to not put hard drives to sleep is often suggested. But random ejects of external drives can have a number of other causes. For example:

https://talk.tidbits.com/t/catalina-users-are-you-seeing-external-hard-drive-disconnects/

https://www.akitio.com/faq/335-why-does-my-drive-disconnect-from-my-mac

https://www.macworld.com/article/232753/what-to-do-if-your-macs-hard-drive-starts-unmounting-itself-unexpectredly.html

while my images are on the external drive.

So, external drive goes asleep (if allowed), lrC goes to access a photo, no drive!

You need to check out if the hard drive is allowed to go asleep, to save energy, when MACOS thinks it is not in use.

https://www.lifewire.com/use-energy-saver-preferences-pane-2260733

Thinking about that, and googling. 
Energy saving preferences, do not allow drives to sleep due to inactivity.

Note that LrC may not be actively communicating with that drive while LrC is running. The program is nit on it, and your catalog may or may not be on it. If your images are on it, well, LrC does not access those files very often.

Define ejecting.