Probably; LBJ was an old school Democrat in the New Deal mold, though that's probably not going to be enough to have him cross the line in 1960 barring unforeseen circumstances. He'd undoubtedly do better in the South (as well as the West) seeing as he was the Senate Leader that stalled the passage of the CRA (no matter how much he'd have wanted to support it), but it may also hurt him with African-Americans (and the North) if the Democrats don't put a decent Civil Rights plank into their platform that year. And without Kennedy, Nixon probably won't choose Lodge, instead moving to another North-Eastern politician like Rockefeller. Overall, Nixon's probably going to top LBJ; perhaps by a greater margin than what JFK won over him.
If somehow the DNC gets deadlocked or LBJ doesn't run for one-reason-or-another, Symington is probably a decent compromise/replacement; he did after-all receive Truman's endorsement, though he's going to have a hard time holding down the South if he doesn't campaign in segregated spaces.
Hilariously (if we're going to go down an implausible route), it would be interesting to see Stevenson get a third shot at bat; made even more hysterical if he were to unexpectedly win.