The lady was behind the right door. This is because, if you truly think about it… you realize that all stories will end hopefully happy. So this is how it goes, he marries the girl behind the door and lives. If the princess really loves him, then she will be happy just to see him alive and happy. Obviously she will be heart broken and sad, but its all because of her father. It may take time for her to understand that, but once she realizes it, she’ll see that its better to have him alive and happy with a beautiful girl, than torn up into bloody pieces dead. According to the story, “She also knew who the lady was. The lady was one of the loveliest in the kingdom.” So most likely she knows the girl, and knows that if she can’t have him, than the loveliest lady in the kingdom should.