I'm not so sure. Lex has had years of experience with Superman and is pretty much an expert on Kryptonians because of it, and he more times than not is not going to beat Superman in a direct confrontation that he's well prepared for even with exploiting Superman's well documented weaknesses. I don't think a week is long enough, especially since, unlike Superman, Surfer has the ability to sense the workings of any devices Lex has come up with from afar via his cosmic awareness and ability to read energy signatures, and the means to simply transmute them and deactivate them. I think eventually Lex could put something together (like Doom did), but it's definitely going to take more than a day, or even 7 days.
That said, pre-crisis Lex would take Surfer in the amount of time it takes him to put a spring in a tin can, squeeze fresh orange juice on it, and then place a mirror at a particular angle so that when struck by sunlight it emits a beam that cuts Surfer off from his power cosmic and incinerates him.