To have the same color palette between Lightburn and Adobe Illustrator, you can use the lightburn-layers file from the Lightburn forum, thanks to hwk44.
On Windows, you can save the library, for example, to C:\Users\<user>\AppData\Roaming\Adobe\Adobe Illustrator 25 Settings\en_US\x64\Swatches, so Illustrator can always find the library.