IIRC, current Catholic view is that Satan got upset that God treated humanity so nicely, to the point of giving us his only son to murder in order to redeem us. But earlier Christian views, and Judaism, has no war in Heaven. Satan was not cast out, is not in charge of, or trapped in, Hell. Satan was the Judaic version of Nemesis, the angel God sent to test mortals.

Also, Lucifer as a name for Satan is a mistranslation. A Hebrew prophet tried to warn the Babylonian king not to make the tower of Babel. He used an analogy the king would recognize, and compared him to a myth from the Babylonian pantheon. The pantheon was ruled by the two brightest celestial bodies, the sun and moon gods. The third brightest celestial body, Venus, tried to usurp them. His rebellion was put down, and he was forced to repeat his unsuccessful coup for eternity as punishment. This is a reference to the fact that the inner planets, Venus, and the as-yet undiscovered Mercury, never fully cross the sky. They rise, traverse, and then reverse and set the same direction they rose from. The whole of the myth wasn't spelled out in the Bible, but enough was described that it did sound very similar to the war in Heaven, so a translator assumed Lucifer must be a name for Satan. They liked it so much they sprinkled it around in some other places top. Which is how Satan came to be known as Venus/Lucifer the evening/morning star.