Low On Hard Drive Space After Adding Photos to Library On External HD

You need to do an inventory on what is taking up space on your internal drive.  If you are running OS 10.14 (perhaps earlier as well), you can go to the Apple in the upper left corner and select 'About this Mac'  Once open, you can select 'Storage' and it will provide a utility to how the space on your internal drive is being used.

You can also go the Lightroom Classic Preferences-->Performance and you can see how much space is allocated to Cache.  There is an option to 'Purge' the cash.

Thanks. I had over 15 GB of free space before I imported the photos, so the imports have used over 10 GB of temporary cache, I'm guessing? Will look into the purge cache function. Why does this cache exist on the internal drive instead of the eternal drive where the catalog and photos exist?

I don't know the answer to that question, but 15GB free space on your internal drive may create lots of issues.  How big is your internal drive.  Best practice says to never use more than 80% of the space of a drive  But you can look at the cache, if I recall and see what is there

as mentioned 15gb of free space on your startup drive isn’t enough.  You should maintain at least 30gb, usually you will start to get warnings about the disk being full if the drive has less than 10% free space, and even sometimes at 20% if your startup drive is small.  Better is around 50GB.  macOS uses a lot of cache files to speed things along.  If you only have 8gb of ram, even more important because macOS will be creating a lot fo swap files and use a lot of virtual memory.

Lots of articles about how to free up space, this one from apple .... https://support.apple.com/en-us/HT206996

Also Time Machine uses a feature called snapshots which store local copies of data on the drives being monitored if the Time Machine drive isn’t available. I myself was bitten by this one, as I found out Carbon Copy Cloner was also using this new feature of the OS.  These can get pretty large.  If you use Time Machine you might want to search for info on Time Machine snapshots. I had over 150GB of space being used on my startup drive by these snapshots.

I don’t have any answers on your dilemma, but you may want to put your catalog on your OS drive and keep your images on the external. https://helpx.adobe.com/lightroom-cla...

Are you "SURE" you had "Add" selected in the import dialog window. Sounds kind of like you had Copy or Move selected.

Most likely it is the Camera Raw cache.