From some reading, doctors think Lincoln could have been saved today, the theory is the doctors, then, caused as much damage as the projectile
It really depends on the path the bullet took through the brain. If the bullet went in straight and missed the arteries or skidded around the inside of the skull then maybe he could have survived. But if the bullet took a diagonal path through both brain halves it would be extremely unlikely thst he would survive.
But the bullets were usually pretty dirty having picked up lint and dirt. The piece of skull with hair etc in it would be dirty too. Not sure if the bullet was patched or not but the patch would be another source of problems too. Then of course the sanitary practices and wound care was pretty minimal back then too. So even if he survived being shot he would have likely died from infection.