I do this every day, using iCloud as an off-line backup. I used to just do Time Machine every day, which I still do, but iCloud is like $3 a month for offline backup (burn the house down and your files are safe) for 200 GB.
But it is a little different, because it is not really designed to be a backup. Apple sees iCloud just as a cloud hard drive. Move a file there and you still have just the one copy, only now it's in the cloud. That's not really a backup then, now, is it?
To use it as a backup is pretty easy, though. Just duplicate your file and drag the copy to iCloud (instead of simply dragging the original, which just moves the file to iCloud).
I drag new copies every time I finish editing a LPX project, and since i have been burned by tracks being missing that are also missing on the backup before, I now save a new copy every time (200 GB, so plenty of room).
And sure, LPX has multiple backups, but hmmm. Which backup will have the missing tracks? It's like choosing the lady or the tiger. Guess wrong and the backup you open might be the wrong one, and you only get the one chance. And you can't revert to that backup without losing recent work.
But if you keep every new edited copy on iCloud, you're covered. And it is a lot faster and less cumbersome than trying to find the right backup on Time Machine.
But your original question may be that you have synced the desktop/docs folders only. I don't know if you can sync the LPX projects folder or not, but that is probably where the LPX projects reside on your Mac. If you could sync it, that's great, and will solve your issue, likely. But I recommend just dragging a copy of each edited project to iCloud, so that you have every edited version available. It's all in one Finder window, Click, duplicate, and drag it to iCloud manually in the sidebar. Easy peasy.