Does Lucifer work for Satan?

Satan can do nothing without the Light.

Something is working for a criminal to breathe.

The original meaning or ‘man’ was genderless meant any human person.

Hu means to BE.

And Lucifer is not one of them?

I would also like to mention the theory of the Meta-God or multiple face God.
One being Satan, or being Lucifer, one being Amaymon.