I don't see that. The Joker exists totally as a mirror to Batman. He has no identity except as Batman's opposite, a force of pure evil and chaos cloaked in cheerful imagery to contrast Batman as a force of good cloaked in fearsome imagery. The new movie may have tried to give him a story of his own, but I see a ton of reviews saying that the movie ultimately has nothing to say. The Joker's fundamental nature is to be a blank slate, a pure embodiment of the chaos Batman stands against, with nothing else to get in the way. The only success anyone's ever had at creating an alternate role for him was through the creation and development of Harley Quinn, making him the embodiment of toxic masculinity and sexual abuse that Harley is initially victimized by and ultimately comes to defy and liberate herself from -- but even there, he still exists only as the contrast to the real protagonist.
Lex Luthor, on the other hand, could totally exist without Superman. The essence of the Silver/Bronze Age version of the character is that he could've been a truly great, heroic (if arrogant) man in his own right if he hadn't developed his obsessive hatred for Superman -- or, in some versions, a conviction that Superman was a danger to humanity and needed a worthy archvillain to balance him out. The essence of the post-Crisis billionaire-industrialist version of Luthor, on the other hand, is that he was already the king of Metropolis when Superman arrived and became the first person ever to exceed Lex's power and fame, making him a rival Lex could not tolerate. In both cases, the essence of Luthor's story is that he was already on a path to greatness (for good or for ill, depending) and was diverted from that path by the arrival of Superman (or Superboy) in his life. His obsession with beating or destroying Superman is not the only thing that defines him; rather, it's the fatal flaw that gets in the way of everything else that could have defined him.