With minor variations, most Christian denominations generally believe that:
- Satan, Lucifer, the Devil, the Serpent, etc. are all the same being.
- Lucifer rebelled against God.
- One third of the angels went with Lucifer.
- Lucifer, Michael, and Gabriel are archangels.
Obviously Lucifer (and presumably the other archangels) have free will.
What isn't obvious is whether:
- Lucifer was a leader of a third of the angels, and they naturally went with him.
- A third of all angels individually chose, of their own free will, to join Lucifer.
Do any denominations specifically teach one way or the other?
(Do angels have free will? asks a similar question, but the answers don't distinguish between Lucifer and angels in general.)