"The reason he hasn't is because of his ego. You see after casting out Lucifer, Lilith and the rest God went on to create something, namely mankind. Lucifer with his ego is trying to prove he's better than God by corrupting God's creation, meaning humanity. If Lucifer can get more souls oh his side of the ledger than God has on his, he'll launch his little war but only then."
"As for Lilith again? Its not a matter of usurping her power. Lucifer would have to absorb it. The equivalent to devouring his sister completely. He tried once to trick his sister into giving up her power and taking it that way by having a demon knight suit of armor made. He had the Blacksmith demon infuse the armor with his power, he then made a pact with his sister for her to put all of her power into it and he promised to do the same with his power. Lucifer and Lilith were then to take turns wearing said armor and rule all of creation. The only thing was, of course both of them cheated. They both only put half of their powers into the armor and planned to use their weakened powers to destroy the other and take full possession of the demon knight armor. Except of course with both of them cheating they found they were stalemated and couldn't gain the upper hand.
The armor was eventually smuggled out of Hell to a secret hiding place so neither could gain the power it contained."