Its actually the richest and wealthiest bad guys who have the most fragile egos. Look at Trump and Musk.
Its the same reason Joker is so obsessed with Batman. Batman is dressed as a scary demonic creature and is dark and brooding and takes life so seriously. That is everything Joker is not. Batman gets under his skin in a way no one else can, because no one else can challenge him.
Superman is the only one that can get under Lex's skin, because Superman is pure of heart and a genuine good guy. Lex can't fathom someone with that kind of power would be that pure. Lex can't buy Superman, and he can't kill him, and there is no one in Metropolis that is as big of a threat to Lex's power as Superman is. Like with Joker and Batman, they are each other's opposite number.