Depends... I personally believe it was Archangel Michael only because it was a war between the angels. I mean when humans go to war does God himself deal with them or do other humans?
Lucifer was Satan's name when he resided in heaven as the 'light bearer'. Light referring to knowledge, Lucifer wanted man to be able to acquire knowledge more easily rather than learning it through life lessons as Christians are intended to learn and grow. His desire to fulfill his duties in a more easily manner caused him to challenge the ways of heaven causing the other angels to fight him and cast him out. Michael-'like god' was the one who ultimately defeated him.
Thus, if you come across Satin worshipers or Luciferians, they will most like point towards self knowledge and self growth as their reasoning for their worship of him and not that they are evil or anything of that nature.
Having done some study into Angelology and Demonology, I'll offer a couple of observations.
If memory serves, the "Son of fire" statement is classically attributed to Azazel, and not to Lucifer. Interestingly, Azazel is also known as one of the Grigori who fell significantly after the creation of Man, in the days of Enoch.
Lucifer has also never claimed the title of Satan in any lore that I've seen. You can link that title to Sammael, Beelzebub, and Belial among others, but not to Lucifer -- whose only biblical appearance is in one questionably rendered passage in Isaiah.
"And the great dragon was thrown down, that ancient serpent, who is called the devil and Satan, the deceiver of the whole world—he was thrown down to the earth, and his angels were thrown down with him." Revelation 12:9
Except in Christianity he created his own little world or so that's horrible and painful and he sits at a tea party or playing his fiddle for Hitler and other horribles.
