The king of pride? But what's so interesting about Lucifer's character is that he doesn't come off as the 'sinnful act of pride' in the show.
This isn't a man who wants to become god, who embodies the other sins in a self-circled manner; He's an upset divorced father ruling over hell —Disappointed in what has become if his kingdom.
So Why is he the sin of pride? You would assume someone who embodies that would be self centered, and believes only in his own achievements. And yet he shows more care — and pride — for what his daughter can accomplish than he seems to do for himself.
He talks about how Heaven wouldn't listen to him, which applies he had similar ideas and wants, but heaven wouldn't care. Why would someone so prideful care more about the right thing and his own people.
It doesn't make sense at the moment.
This is definitely open for interpretation. I will say I am not a Christian myself, I can't say I have analyzed the bible to know everything to dissect about Lucifer and his Sin.