Does LR Library fill your computer drive?

Apple has no idea what's taking up all my memory.

That's surprising as it is trivial to find out what files are taking up space. A very simple thing to do is to do "about this Mac" from the Apple menu. Click on the storage menu and click on "manage". Look at what is taking up the biggest space. Generally this should be "documents" which will include your Lightroom catalog and its many backups. It is possible that unwittingly you are storing all your images actually on your internal disk, so that is something to watch out for. Also, you do not need to keep more than a few catalog backups.

One major problem I think is that Apple ships its laptops by default with a way too small SSD of only 256 GB in it. That is bound to lead to problems very quickly.

When something unknown is taking up a large amount of space, there are several ways to find out what it is.

You can use software like Disk Inventory X or Grand Perspective, which give you a visual map of which files on your drive are taking up the most space.

Another thing I've done is use the Mac Finder itself:

1. Open a Finder window of your Home folder.
2. Choose View > Show View Options, turn on Show Library Folder, and turn on Calculate All Sizes. This makes the Size column show the size of all items in the window, including folders. It may take a few moments for the Mac to add up everything inside all of the enclosed folders.
3. Sort by the Size column, descending. Now the biggest folders are at the top.
4. Expand the biggest folders; the largest items should continue appearing at the top. Keep expanding down until you find very large files or folders that you don't need.

It is possible that your backup choices are adding copies of your catalog file and, over time, take up some significant space.

In the past that might have been true, but if it's a current version of Lightroom those backup copies should be ZIP-compressed and rather small.

If the disk space problem is due to Lightroom, some candidates are:

• The previews file.
• The Video Cache hidden in the Libraries folder at (username)/Library/Caches/Adobe/Lightroom/Video
• The Camera Raw cache at (username)/Library/Caches/Adobe Camera Raw

Both caches can be limited in Lightroom Preferences, under Performance.

Both of those folders grew over 1GB on a Mac that had Lightroom on it for less than a week, because I imported many images and videos.

But you might also find that other programs have accumulated a lot of data in the Caches folder. That's normally good for performance, but not if it gets too big.

Perhaps you could do a search of your internal hard drive using Mac Finder or related utilities to see what is taking up all that space.

And please confirm that your photos are really really really being imported to your external drive. Don't just say "YES That's where I put them", you need to look and see with your own eyes AND CONFIRM that they are really on the external drive and not on the internal drive due to some mistake. Look in the Lightroom Folder panel and make sure all the folders are on the external drive and none are on the internal drive.

How big is the internal drive? How much space is free on the internal drive? How many photos do you have in Lightroom? What size files are the photos when they come out of the camera?

The Lightroom Previews.lrdata folder can get quite large dependent on your Catalog settings for Previews.

The catalog file is relatively small.  You can look for it in Finder with the .lrcat file extension.  It is possible that your backup choices are adding copies of your catalog file and, over time, take up some significant space.