Lucifer Morningstar's History
Eons ago, Lucifer Morningstar rebelled against the Kingdom of Heaven, and was cast into a shapeless void known as the Chaoplasm. The Chaoplasm was transformed into a desolate and barren expanse known by many as Hell, the final destination for damned souls. Here Morningstar ruled, awaiting the day he could be freed.
Lucifer was forced to share his power after the Great Darkness's return. A Triumverate was formed, with Azazel and Beelzebub, but Lucifer retained the majority of power.
Leaving Hell
At one point, Dream of the Endless entered Hell searching for the Helm that had been stolen from him when he was imprisoned. After Dream recovered his helm and slighted him, Morningstar threatened to destroy Dream.
Lucifer eventually abandoned his lordship over Hell. Lucifer had ruled as lord of Hell for ten billion years. Over that time, he had manipulated the various demons of Hell against each other, provided a place for dead mortals to be tormented, and led the war against Heaven. However, at some point during his rule, he had become bored with this existence. He became tired of the various stereotypes that mortals held of the devil, such as the idea that he purchased and traded for souls, which were largely untrue. He also resented the assumption that he caused the evils that humans did- he did not, in fact, have anything to do with the actions of the mortals who ended up there, he simply punished them. He had become tired of his reign over Hell, and felt it an unfair punishment that he should have to rule there forever simply because he once rebelled. These feelings were catalyzed when he was visited by Dream. Lucifer expelled all demons and damned souls from Hell before locking Hell's gates and handing over the key to Hell to Dream of the Endless.
Life on Earth
Eventually, control of Hell was handed over to two Angels, Duma (the angel of silence) and Remiel ("who stumbled rather than fell"), while Lucifer simply retired to Earth, specifically to Perth, Western Australia.
Now running a piano bar called "Lux" in Los Angeles with the assistance of his Lilim female consort, Mazikeen, Lucifer is portrayed as sophisticated and almost charming, similar to the stereotypical Christian devil. Beneath his charisma, however, Lucifer is a deadly and Machiavellian character, with no regard for human life or indeed any life other than those he can use to his advantage: a proud and vindictive fallen angel who has no qualms using powers second only to those of his father, Yahweh. In fact, Lucifer is described as having been the wisest, most beautiful and most powerful of all the angels in heaven, and he retains these traits even after his fall. Despite his egotistic and narcissistic tendencies, he does follow something akin to a code of honor- there are few beings in existence he respects (his brother Michael and the Angel Duma among them) and only two he could be argued to care about (Mazikeen, his consort, and his niece Elaine), though his actions on their behalf are almost always for his own benefit, and it is doubted by all that he would help them otherwise. He also refuses emphatically to lie (which he considers crass and undignified), insists on paying back debts, and keeps his word- though this must not be confused with virtue.
Lucifer's "restful" retirement was disturbed by a series of associates from his past, and after various catalytic events, he endeavored to create a multiverse in competition with that of (and presumably against the wishes of) his father, Yahweh. This puts him on a collision course with several powerful mystical entities that have a vested interest in the new creation and draws the angelic host into the fray - including his brother, the archangel Michael Demiurgos and his niece Elaine.