An Angel with a shit job
If you really think of it he’s a child of a father thaleddidn’t want to do the hard job. God himself didn’t want to be ”the bad guy” he sent his son who he didn’t know what to do with down to hell as a punishment. God takes all the glory and let’s Lucife, an Angel to be villainised for doing a dirty job. He punishes the bad people in their afterlife the way the bad people messed up when they were alive. Luci punishes the guilty. Remember, he's an angel. Someone has to do the dirty work of his father's creations. If he didn't the guilty would be set free upon the innocent once again. So no, he's not the “bad guy” he's just someone to blame. The worshipers who kill for him or do wrong for him will be punished by him because that is not what he wants or is about. The same for the ones that give hate, hurt others mentally as well as physically and killing in the name of God will be going to hell to get punished for their crimes. God wants nothing to do with them. That's why he threw his son down to hell so he didn't have to deal with it.
A psychosis based in uncontrolled narcissism, inflated arrogance and a perceived need to subjugate and/or ridicule other individuals deemed to be inferior or unworthy.
That is a description of a person who has a God complex.
Yes there is a devil complex but that is based off of the image of him being this evil monster when he's not.
Some villains are proud of the fact they're villains, fully admitting they're evil and boasting about it. But some go even further, by claiming to be who many consider the ultimate villain, the Devil himself. Or a God of Evil, or a high ranking demon or demon king. In short, they have a Devil Complex.
That's not who he is at all. He's doing what he was forced to do because his father disowned him and threw him away. A fallen angel. A child of neglect of not ever being forgiven but sees his very father giving everyone else the chance to get forgiven.
Lucifer is not a bad person. He just has a shit job.