I doubt he would have lost. If anything, You should read this. Johnson thought there was a conspiracy too, and found out after he took office who may have been behind it.
Personally, I don't believe Castro was behind Kennedy's assassination, but he did have good reason to be. The Kennedy's, especially Saint Bobby, had been trying to kill him.
Johnson knew nothing about any of that until after he became president.
LBJ could play bare knuckle politics with the best of them, but compared to Bobby Kennedy, Johnson was a Boy Scout.