Yes, we do believe in the literal Satan/Lucifer. We believe that he does exist. In Theistic Satanism most see him as God and the creator. I may be a Theistic but I do not see him as the creator but a God of other things.

There are some Luciferians that believe that he exists and some do not believe that he exist. I am not sure how Luciferianism can also be atheistic.

In LaVeyan Satanism they do not believe that he exist. They view him as a archetype representing pride, carnality, and enlightenment.
What bothers me the most is when The Church of Satan says they DEFINE Satanism – (They do not define Satanism). They say that Theistic Satanism is an oxymoron when it has been around way longer than LaVeyan Satanism.