How would you describe the tone of "The Lady or the Tiger?"

You could argue that the story is playful, serious, and curious. The story has a playful tone in that the language is old-fashioned and Romantic but with a satiric and sometimes sarcastic intent. The king is "semi-barbaric" and was "given to self-communing." In other words, even if he is only barbaric some of the time, he is barbaric in principle. So, he is barbaric, plain and simple. He only communes with himself and this means...

You could argue that the story is playful, serious, and curious. The story has a playful tone in that the language is old-fashioned and Romantic but with a satiric and sometimes sarcastic intent. The king is "semi-barbaric" and was "given to self-communing." In other words, even if he is only barbaric some of the time, he is barbaric in principle. So, he is barbaric, plain and simple. He only communes with himself and this means that he doesn't listen to or take advice from others. He is like, or considers himself to be like, a semi-vengeful god. Stockton uses these phrases to dance around the direct meanings and get the reader to think. He is also playing with the idea of interpretation and choice. 

Note that the king allows the courtier a choice between one of two doors. Like a semi-barbaric god, he gives the courtier semi-free will. So, the courtier has choice but that choice is limited. What is Stockton doing here? It seems like he is being purposefully playful in provoking the reader to analyze what he is doing. Is it an invitation to the reader to consider what free will really is in a religious context or in the political context of kings and subjects? Just as the courtier must choose, the reader must choose. 

So, as much as the author is being playful and making satiric and sarcastic suggestions about human exploitation of power and the limits of free will, he is also asking serious questions about how far (or how little) humanity has progressed. And playing (seriously) with the notions of free will and choice, Stockton leaves it to the reader to decide what the princess's final decision is. Even if this is a tale about a kingdom long ago (and this is not clear either), would a modern reader conclude that the princess directs the courtier to the tiger? And if that is the case, what does that say about the modern reader's perception of human frailty? This is the beauty of the story. The author is playful, satiric, and serious. His tone combines all of these notions as he asks the reader to think for him/herself. Given that, you could also argue that he subtly shows his curiosity about how the reader will interpret the story and/or what the reader will conclude about the princess's decision.