Insufficient Memory Crash on new MacBook

First an inquiry, looking at your first screenshot

So, that is basically a search for large files. And those three identically named catalogs would be in different folders on that one hard drive. Why do you have three identically named catalogs? And I do not think one is the backup.

You might want to clean that up. Oh, and if they are different catalogs, then rename at least two of them, and consider migrating to one catalog.

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Second, a related inquiry from that screenshot. Two archived (zip) catalog files, Once again  same name, so I assume different folders (or perhaps in Time Machine). So are those backups? Storing backups on the same hard drive as the primary file is begging for your house gremlin to crash hard. When that occurs, both the original and the backup will be gone. Might want to backup to an external (other than one with your catalog, should you move it/them)

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Third, a rant. Photographing your monitor to share a screenshot is bad form. Yours worked way better than most, they were usable. but see:

https://support.apple.com/en-us/HT201361

Ok a few things.

This is the Photoshop forum, not Lightroom.

Second, storage and RAM are different things. RAM is working space, storage is the internal SSD.

Third, your computer probably has 8GB of RAM and you got it with 256GB of storage, both the cheapest configuration. Lightroom is going to be cramped with that, 16GB of RAM is much better.

Fourth, you desperately need an external hard drive for storage. MacOS uses drive space to augment RAM and when you run out of both, typically applications and sometimes the whole computer can crash. You are out of drive space and out of RAM.

Buy a second external USB hard drive, you'll need one with USB-C or need a cheap USB-C dock to plug it in. A 4GB drive is around US$100. Move all of the Lightroom files to the second drive. Free up as much space as possible on the internal MacBook drive. This should help immensely.

Files aren't in RAM. What is your system configuration? Best way to give us that info is a screen shot of your ABOUT THIS MAC box. Please don't post photos of the screen, please post normal screen shots. 

Do you get the same error if you access from your local drive instead of the external?