To me, Lex should always be diametrically opposed to Superman in every possible way. They both have roots in Smallville, but after that their lives go in very different directions after Lex's bungled experiment and his denial of his own fault in his baldness drive him over the edge.
Superman relies (primarily) on his phyiscal might. Lex is a man of intellect.
Superman came from a farmer's background, rose among the people and has strong roots in the working class that he draws upon as a source of inner strength. Lex despises the working class he rose from and built a multi-billion dollar corporation partly from spite to that background and partly from sheer boredom.
Superman lives to help others and keep the world safe and orderly. Lex lives to help himself and enjoys making Superman's world chaotic.
Superman reveres life. Lex sees life as inconsequential save when it's his own.
Superman needs Lex because Lex reminds him of what he could do with his abilities if he walked a selfish, self-serving path. Superman believes deeply that he could redeem his friend, make him the good man he truly could be. He considers Lex his friend despite every attempt on his life, despite every evil scheme. Superman is never angry with Lex, just saddened by him. And that makes Lex
crazy. Bad enough this alien, this freak of nature upstages his natural genius at every possible turn, worse still that people flock to this abomination rather than the natural human genius of Lex Luthor, but the fact that this spit-curled godling has the nerve to
care, to still want to save him, to still think he's worth saving. . .it drives him mad(and secretly makes the Greatest Criminal Mind of our Time wonder if maybe--just maybe--he really is on the wrong path).
Bruce Timm and Paul Dini once said the best Superman stories come from the notion that Superman uses his power (which represents the power we all have) responsibly, and his best adventures come from the notion of running into beings that use their power irresponsibly. Nowhere is this more evident than in the character of Lex Luthor, a man who could do so much good, but can't and won't because he doesn't see anything beyond his own wants, needs, and obsessions.
Just my $0.02 and change, for what it's worth.
-Def.