I agree - Lincoln was the luckiest man in the world to have had a combat veteran checking the door at that moment. Booth had done some preparation work to gain entry to the room, and had an (unwitting) accomplice holding a horse for him outside. Grant foiled the attempt spectacularly, overpowering a man with a knife after taking a bullet through the hand. (Booth probably should have had more firepower than that single-shot pistol.)
Chances are
somebody would have been there - the Lincolns were more comfortable with company at the theatre. But whom? Mary Todd Lincoln was crazy as they come, and probably hastened Lincoln's death just from his having to have her around. (On the other hand, perhaps Lincoln was extremely
unlucky to have survived the assassination atempt.

) They may have ended up with some wimpy bureaucratic clerk and his eight-year old daughter for company that night!