Yup. Something like that. Satan was kind of the overlord of things, got tired of the infighting, and packed up shop to go exploring for a while (according to what we've heard), while Lucifer was second in command and brains of the operation. He's been out of commission since pissing off Death (Fi's mother) and living, quite literally, as a bum outside of the twin's apartment building.

Beelzebub has been chairman of the Board since, or was until he tried to take Fiona's brother, Eliot, off. Fiona and Eliot killed him and Lucifer used that release of power (and a very well-mapped spell) return himself to his former status and get back in the game. Supposedly, this is so he can better protect Fiona and Eliot; surprisingly, that seems to be the truth at least to a reasonable degree.