Everything from Dante's Inferno to Little Nicky show Lucifer as the ruler of hell, having his demons inflict punishment on sinners. It's a well-known fact that he's the ruler of hell, so how could this be a misperception?
First off, show me one verse in Scripture which says that. In fact, it says the opposite.
Then the devil, who had deceived them, was thrown into the fiery lake of burning sulfur, joining the beast and the false prophet. There they will be tormented day and night forever and ever.
So hell is a punishment for Lucifer, not a domain to rule over. So where does the idea of him ruling over it come from? According to Got Questions, it basically comes from Dante's Inferno. But as this other Got Questions article says, it's not exactly a biblically accurate novel. It takes inspiration from multiple sources, from the Bible, the Quran, and other traditional ideas of Heaven and hell. As such, it has quite a few inaccuracies. Seeing as Scripture doesn't say much in regard to describing the place, and Dante's Inferno was written between 1308 and 1321, it went on to heavily influence society's views of hell.
Until the Judgement, Lucifer is able to walk back and forth between Heaven and Earth. So does Lucifer rule over anything? Earth. Lucifer rules over Earth. "But wait!" you're probably thinking. "Doesn't Jesus rule over Earth?"
“I don’t have much more time to talk to you, because the ruler of this world approaches. He has no power over me"
That is Jesus talking, referring to Lucifer as the "ruler of this world". Okay, so he doesn't exactly name drop Lucifer, but Paul makes it Claritin clear. Not only referring to him as the ruler of this world, but as the "god" of this world.
Satan, who is the god of this world, has blinded the minds of those who don’t believe. They are unable to see the glorious light of the Good News. They don’t understand this message about the glory of Christ, who is the exact likeness of God.
However, his reign is not to last, and he knows it.