Exorcists like Fr. Gabrielle Amorth, Fr. Malachi Martin and Fr. James Lebar were all convinced that Satan and Lucifer were distinct demons.
This is also true of Belial, Beelzebub and some of the other Biblical names. Each one is different.
“Satan” in the Middle East means “the accuser” or “the adversary”. (So when the U.S. is called “the Great Satan” in the news, they aren’t being quite as accurate as they could be when it comes to translations.)
According to Fr. Martin. Lucifer is the demon with the big vision so to speak. His plans stretch out over great periods of time and he as “the light bearer” basically pretends he’s God. His symbol is the Scorpion.
Satan is the more direct “hands on” executor of the plans that make up Lucifer’s 'big plan" leading to Anti-Christ.
It’s interesting and since the Exorcists are generally consistent, it’s not implausible doctrinally.
Just leave a little bit of room for possible clarifications on a magisterial level in case the Exorcists were wrong or fooled by demons in some of that information.