The Lady, or the Tiger?

Called the most famous riddle mystery of all time, this very short story poses a dilemma. A man is sentenced to an unusual punishment for having a romance with a king's beloved daughter. Taken to the public arena, he is faced with two doors, behind one of which is a hungry tiger that will devour him. Behind the other is a beautiful lady-in-waiting, whom he will have to marry if he finds her. While the crowd waits anxiously for his decision, he sees the princess among the spectators, who points him to the door on the right with a slight movement of her hand. The lover starts to open the door and…

Did the princess save her lover's life by pointing to the door leading to the lady-in-waiting, or did she prefer to see her lover die rather than see him marry someone else?

(Summary from Wikipedia.)