From the point of view of Theistic Satanism, probably there is no difference.
Classical understandings:
Lucifer = The king of hell in classical magic texts, King Nebuchadnezzar, or a Roman god symbolic of Venus as the morning star. Modern Luciferians would probably try to make him into something of a Promethean figure rather than directly equate any of these understandings.
Satan = Archangel Samael's title, or those working under him directly. There are more than one.
The Devil = Equivalent to either of the previous, but also the spiritual boogeyman of Christianity. Largely a pejorative statement in reference to the Satan/Lucifer hybrid.
Spiritually, for me, they're synonymous. The medieval texts equated Lucifer functionally but did so in the context of obfuscation in a time where doing a rite to Satan would probably get you killed. If you could put two and two together you'd figure it out anyway by definition. So, I guess it's about what time in history you'd like to go with. I like the Lucifer/Satan equivalency, but I am interested in the old occult.