Definitely not. Luther is a work of fiction. The creators crafted the story and its elements to provide viewers with an exciting and thrilling viewing experience that doesn't have a basis in reality.
Clark and Lex were friends at the beginning in the comics. But as the story progressed, Lex's character changed, and they became enemies. This transformation was driven by Lex's mistrust and his own ambitions.
Yes, in some storylines, Lex and Superman can be portrayed as having a complex relationship that might involve moments of friendship or uneasy alliances.