I'm not sure they'll even call back the Speaker reference. That was a throwaway Cat Grant line at the start of season 3, I think it was, and I believe the show was under different showrunners then anyway. It's too minor a detail to expect them to build all their plans around it.
In the main DC Universe as it existed prior to the Flashpoint/New 52 reboot, he did become US President for a few years. Clark's Smallville friend Pete Ross was his vice president, and a retired Black Lightning was his secretary of education.
As I mentioned before, Lex is in prison last we heard. If he'd escaped, it would've been big news to the characters, so we'd know if it had happened.
Well, unless he's had himself replaced in prison with an impostor, like the Joker did at the start of The Killing Joke.