Idisagree with you.
Lex is a core member of any superman cast. He should be in every movie... but he should only be the primary villain in the opener. But in sequels he should be that man plotting in the background. All the while other villains are doing their thing with Superman. Infact, this is what made the TAS Lex so absolutely perfect. He was never the primary villain, but always the one pulling strings.
Even in a movie franchise, Superman's relationship with Lex is just as important as Clark's relationship with Lois. Lex is a core supporting role, after the intro movie (which has been done).
I feel that the Lex-Lois relationship could be interesting in a 'wrath of kahn' like reboot (ie. same players, but the universe is tweaked slightly). As someone pointed out, the difference is that SR has loose ends, while STTMP didn't.
I think the easiest way to do this, is have Jason and Richard go into hiding... because Lex knows, and is still at large... relegate them to the Kent farm, with Ma. Meanwhile, go on with a Brainiac invasion from NK. Pardon Lex, because of his knowledge of crystals. Have a huge Brainiac/supes/military brawl while Lex figures out where the son of superman is hidden, and tries to assasinate him. Superman uses the scraps from Brainiac to revive the fortress, and send Jason to kandor, where he can be cared for.