The point of the story is that the reader never actually finds out what happened. The Princess knows which door hides the Lady and which hides the Tiger. Thus, she will be making the decision for the Courtier. We know she loves him, but also that she is passionate and jealous in disposition. Neither choice will make her happy. If she points to the tiger door, her beloved dies. If she points to the other door, he marries someone else and she is left feeling jealous and miserable. You could argue either side of the question:

Lady: In this case, your main line of argument would be that, if the Princess genuinely loves the Courtier, she would not want him to die a painful death and thus would decide to save him, even if it meant his marrying someone else.

Tiger: In this case, you would emphasize the hot-blooded and jealous nature of the Princess and argue that she would prefer the Courtier dead than married to someone else. You could also argue that she would know this choice would please the King, who is her father.