That is a very good question because it brings up an important point. Contrary to popular myth, stealing a horse has never been a capital offense in any state or territory. Lynching horse thieves did occur but not by lawmen. If a lawman captured one he would be duty-bound to bring him in, charge him and stand trial. That’s not to say a mob might storm the jail and lynch him but that was usually if the charge was something more serious like murder.
If a man was being lynched the hangmen were probably amateurs who would sit you on a horse, drop a loop around your neck, throw the rope over a stout tree limb and anchor it to the trunk then slap the horse in the rump. That would leave you there to die slowly. It was crude and it wasn’t pretty.
A trained hangman would use a good, sturdy rope, build a noose, place it snugly around the neck, placing the knot securely behind the left ear. He would adjust the length of the rope with the man’s weight so that when the trap was sprung the drop would be enough to break the neck. Instant death would occur if everything was done right. A good hangman took great pride in his work.