Booth could have been arrested before hand, his co-conspirators were not the greatest men in a pinch. Say one of them gets picked up before hand, Atzerodt gets drunk a little earlier when he goes to kill Johnson and starts blabbing. Confederate sympathizer overhears and tries to take him out lest he ruin something (even if the sympatico doesn't know what it is, he knows it sounds good for the cause) and gets caught in the act by soldiers. (Washington is crawling with them) Slight interogation, brutal with the suspension of habeus corpus, gets everyones dander up. Security tighter at Fords, maybe Booth busted, maybe he just walks away to fight another day.
If Lincoln doesn't die, I don't think he survives the politicking that goes on after the war. Lot of people ticked off about his policies and heavy handedness, or reverse that, lots of people pissed about the soft line he wants to use on Confederate Leadership. Any which way, he is not the iconic Lincoln passed down through the ages.