The Luthor we're seeing in the movie is closest to the version we've seen in the comics (and animated Superman series) since the John Byrne post-Crisis revamp. Examining his motivations might help clarify Movie-Lex's thoughts.
Lex, as in the film, is no longer a generic super-criminal, but an incredibly successful businessman. His inventions are found at every level of society, from industry to personal electronics and every other niche in between.
When Superman appears, he suspects his motivations; partially because he's an alien, but partially because nobody could be that altruistic without having an angle. Lex believes that mankind should not rely on aliens to save us and solve our problems, but on ourselves. More specifically, they should rely on him.
In short, Lex's motivations and behavior are almost exactly that of Max Lord on Supergirl, though they've bent over backwards to claims he's not just "her Luthor".
The second, underlying motivation is sheer and simple jealousy. Before Superman came along, Lex was the biggest thing in Metropolis, and the single person on whom the most people relied and trusted. Superman's appearance dropped him to the place position, and he can't stand it.
The battle between them has gotten far more personal over the years, but those two core motivations are the center of it. Movie-Lex has similar thought processes, but not nearly as clear, or rational.