Unlike Bat or Super, people like Lex exist. Lex doesn’t hate Super because he’s powerful, he hates him because he’s loved.

Lex’s whole worldview is that the people who are smart and cunning should rule over those lesser. Super’s existence contradicts this by serving the interests of people who are his inferior.

Lex must believe that Super is a fraud who doesn’t deserve his position because otherwise Lex is the pretender.