Dear Mr. Koetting:
I would like to know if the entity known as Lucifer is Azazel. That would be my question.
In my workings though, he has merely answered with the following question: “is it so important to you?” ; all while his appearance suggested being actually the same being, judging from his scalding smirk.
Please let me know 
I am curious about this myself.
He depicts them as separate i believe
No. Originally, Azazel was simply a word referring to the “scapegoat” in the sacrifices on the day of atonement. It wasn’t until much later when Azazel developed into an entity in Jewish mythology.
Or, arguably, an entity stepped forward to claim that name and role.
In my experience and from what Azazel has told me… no.
I’d like to know this too.