First, is it feasible? What would it take to dampen opposition to LBJ's Vietnam policies within the Democratic party? Let's go with the minimum possible change there, so the Vietnam war doesn't become the only focus.
Second, what would he have done differently from Nixon in his new term? Vietnam? Space program (Does he still keep putting political capital behind it? What shape does it take? More moon missions--at least the planned series through Apollo 20? Maybe restarting Saturn produce--my understanding is that the halt in 1967 was supposed to temporary--for a continuing series of moon mission? Maybe a moon base of sorts--one was proposed using modified Apollo hardware?) Domestic policy?
And, of course, spin-offs. Who would oppose him? Presumably Nixon. Would another defeat end Nixon's career or would he somehow land on his feet and run in 1972? Who does run in 1972? Humphrey? Bobby Kennedy (who hopefully wouldn't have been assassinated)?