how her soul had burned in agony when she had seen him rush to meet that woman, with her flushing cheek and sparkling eye of triumph; when she had seen him lead her... After reading this story, it is my opinion, based on the text quote below that the young man chose the door with the Lady behind it. Here is why.
I think that the princess sent her lover to the lady because she loved him too much to see him die. We can see this from her fears about the lover being torn apart and because we know how much she loved him.