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, but Lucifer retained the majority of power.
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 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 his 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 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. So, Lucifer expels all demons and damned souls from Hell before locking Hell's gates and handing over the key to Hell to Dream of the Endless. 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 anyone or anything but himself: 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. Despite his egotistic and narcissistic tendencies, he does follow something akin to a code of honor, refusing to lie (which he considers crass and undignified), insisting on paying back debts, and keeping his word.
Lucifer's "restful" retirement was disturbed by a series of associates from his past, and after various catalytic events, he endeavored to create a universe in competition with (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. Structurally, aside from the meeting in Hell that Lucifer arranges with angel Amenadiel.
Lucifer (2016 TV series)
Lucifer Morningstar stars as the title protagonist/anti-villain in the FOX TV series Lucifer, played by British actor Tom Ellis. In the show, he is apparently bored of his life in Hell, and so he rebels, abandoning the Underworld to go live in the mortal world, more specifically Los Angeles, where he runs a nightclub called Lux with fellow escapee from Hell, "Maze". When a celebrity he did business with is gunned-down before him, he sets out to find out who ordered the hit, but Maze is concerned that he's showing empathy for mortals. He currently assists LAPD officer Chloe Decker in solving various cases, using his ability to compel people to speak their honest opinions and secrets to get what he wants. Meanwhile, the angel Amenadiel appears to Lucifer and tries convincing him to go back to Hell, as he'll have to take Lucifer's place if he doesn't go back.
Lucifer, stay. Good Devil.