I think Lex vs. Iron Man would work well. The dynamic would be different but could be just as intense. Highly disciplined self-made man Lex would hate Tony who is (apparently) an undisciplined playboy who inheriting it. He would hate being compared to the golden boy inventor, especially when he came off as second best. The dynamic would be a little like Stark vs. Obadiah Stane or Justin Hammer but more interesting, IMO.
Stark didn't inherit his fortune. The first iteration, yeah, Howard Stark created it, but since then the companies been built and rebuilt by Tony himself. And Lex isn't supposed to be second best usurping some businessman, he's supposed to be the best and smartest mankind has to offer against what he perceives to be an alien threat. I think Lex vs. Tony would be doing an injustice to Lex.
Plus, almost none of Lex's stories have to do with the mechanics of LexCorp. A "company battle" wouldn't really fit.