Source Vertigology

Lucifer, and I do mean the fallen angel who was the favorite of the Christian God. In the Bible, it tells of him being cast out of Heaven for rebelling against God. It was to be his torment and punishment. Neil Gaiman’s wonderfully creative mind put more to the story.

In the Vertigo (which is owned by DC) Sandman comics/graphic novels the Devil shows up for the first time in Prelude and Nocturnes. He meets Dream of the Endless for the first time when Dream shows up in Hell looking for his helm. It is in the possession of one of Lucifer’s demons who looses the duel. Lucifer tries to prevent Morpheus from leaving assuming Dream has no power in Hell. Morpheus embarrasses Lucifer by pointing out his power, which Lucifer has no power over. For this slight, Lucifer wants to kill Dream.

Source DC Comics

It is in Season of Mists that Lucifer tells that he tires of Hell. He wants to end his torment and he quits. He empties Hell and locks it up. He asks Morpheus to cut off his wings then hands him the keys of Hell knowing that it may or may not destroy Morpheus. He doesn’t care either way. He was found in Perth, Australia. He was speaking to an old man who said he had a shit life but that any one who could paint beautiful sunsets every night deserved some respect.

He returned to the Sandman comics briefly in The Kindly Ones. This is when he is living in Los Angeles and owns a bar named Lux. In the comics it was Remiel, not Amenadiel whom asked Lucifer to return to Hell. An order which he refused in both the comics and the show.

Source Funnyjunk

Lucifer has become disenchanted with presiding over the souls and demons in Hell. More than that he wanted to correct humans of the lies they told of him. He doesn’t buy souls and he doesn’t gets humans to sin because of his influence are at the top of his list. These ideas are consistent through the comics as well as the TV show.

It is revealed in both that the ruling of Hell wasn’t so much a punishment as it was a gift. It was that he was as far removed from the light of his Father and could still be aware of him that made him special. Lucifer turns out to be a decent person despite his trying not to be. He is honorable and pays his debts. He doesn’t lie and he doesn’t kill. He even is capable of love and sacrifice.

Source Comic Book