What happens when I uninstall a custom lot from the launcher?

Hi :)

It doesn't disappear from the place you placed it in the world, it deletes it from your Library. You should also still have it in your downloads folder if you installed it through your launcher. :)

What you saved to the library is still in the Library after uninstalling the world. I don't see what issues it would have unless they had some strange issues before saving them to the library.