Who came out of the lover's chosen door, the lady or the tiger? And why would the princess choose this outcome?

As readers, we don’t know which door the Princess signals her lover to choose.  The story ends before it is told to us.  It’s a little frustrating as readers, but the purpose of the story is to get us to think about moral issues and choices that we make.  If the Princess signals the door with the beautiful woman, she loses her lover to another woman, but, at least, he remains alive.  If she nods towards the door with the tiger, her lover will certainly be killed, and she loses him forever.  So, it’s up to the reader to try to figure out what the Princess does.  Remember, she is described as a “barbarian Princess”, and is that enough to tell us that she would rather see her lover die than in the arms of another woman?  We are left to guess the answer.