1964: JFK versus Goldwater.

[Lincoln Republican]

JFK would keep LBJ on the ticket.  

Dropping LBJ from the ticket would be a foolish political move by JFK and would be resented by large segments of the Democratic Party.  And JFK was not foolish.  

Against Goldwater, JFK would easily be reelected President in 1964, with or without LBJ, but even though there was animosity between JFK and LBJ and between LBJ and RFK, I do not believe that JFK would drop LBJ.  After all, the President and Vice President do not really have to see each other all that often anyway.

The only way that LBJ would not be on the ticket in 1964 would be if LBJ told JFK he would not run again as Vice President.  

Vietnam would become JFK's problem, not LBJ's, and if JFK mishandled the Vietnam issue like LBJ did, then JFK would be the one vilified for causing the needless deaths of thousands of young Americans, not LBJ.  If, however, JFK handled the Vietnam situation well, then JFK would go down in history as a great President.

The Great Society would have to wait, unless JFK took up the issue.

LBJ either retires to his Texas ranch in 1969, never having achieved his lifelong ambition of becoming President of the United States, or runs for the Democratic Presidential nomination in 1968, likely facing younger, more dynamic opponents for the nomination, and if he does win the nomination, attempting to win election as a Democrat, after two terms of Democratic administrations already.

So I would say, under these circumstances, LBJ's chances of being elected President in 1968 would be slim.