Stockton leaves us hanging, ending on the following question:
And so I leave it with all of you: Which came out of the opened door,—the lady, or the tiger?
We know the lady is much like her father, which is to say "semi-barbaric," with his practices strongly favoring his barbaric side. It is, therefore, highly likely that she would do what was in her own interest, rather than sacrifice her needs for another's well-being. We learn that
had it not been for the moiety of barbarism in her nature it is probable that lady would not have been there, but her intense and fervid soul would not allow her to be absent on an occasion in which she was so terribly interested.
In other words, she is completely capable of watching her lover being torn to shreds. At this point, it becomes a mind game. If her lover picks the door she indicates, we might assume a tiger will come leaping out, as she would rather see him die than see him married to her rival. However, the lover would likely know the princess's nature and therefore not pick the door she indicated. In this case, he would choose the door from which would come the lady.
However, what if she anticipated that he would pick the opposite door? Would she indicate the door with the lady, knowing he wouldn't pick it and therefore have the enjoyment of watching him be devoured as a result of distrusting her?
Weighing the odds, the princess's barbarism points in the direction of her not overthinking the situation. Like her father, she probably reasons simplistically, so we could assume she would point her lover to the door with the tiger, and he would be fully aware of this.