The ambiguity of the ending of "The Lady or the Tiger?" is based entirely on the feelings and motivation of the "hot-blooded, semi-barbaric princess." When her lover is in the arena and looks to her for guidance:
She raised her hand, and made a slight, quick movement toward the right.
Her lover has complete trust in her. But how well does he know her? How well does any man know any woman?
Without the slightest hesitation, he went to the door on the right, and opened it.
The fact that the lover shows such complete faith in the love of the princess may be intended to suggest that men do not really understand women very well at all. No doubt, different readers would have different takes on this story, depending on their gender.
Now, the point of the story is this: Did the tiger come out of that door, or did the lady?
The princess knows which door conceals the tiger and which conceals the lady whom she passionately hates.
The girl was lovely, but she had dared to raise her eyes to the loved one of the princess; and, with all the intensity of the savage blood transmitted to her through long lines of wholly barbaric ancestors, she hated the woman who blushed and trembled behind that silent door.
The author keeps using the word "barbaric." It is up to the reader to guess whether the beautiful lady comes out and marries the princess's lover or whether the tiger comes out and tears the poor, trusting man to shreds. In either case, the princess is going to have to observe an event that will be very painful to her. Would she rather see her lover married to the lady? Or would she prefer to see him torn to pieces by a tiger? How much does she really love this man? And would the strength of her love make her choose to save him or sacrifice him to another woman?
The author takes pains to characterize this princess as a woman with a strong and passionate nature. A less "savage" and "barbaric" woman would undoubtedly choose to do the compassionate and enthical thing, which would be to save her lover's life and allow him to enjoy happiness with her rival.
The reader is not really required to guess what happened but to guess what the princess decided to do. The setting is of extreme importance to this story. It takes place in "the very olden time" and in a barbaric land. There seems to be a strong possibility that this princess might easily decide to have her lover killed before her eyes. She has probably witnessed many such spectacles already in her young lifetime. She may have made her decision long before she entered her seat above the arena.
But, on the other hand, if she didn't care enough about her lover to be able to contemplate watching him killed by a tiger, why should she care about letting him marry the other woman?
The story ends inconclusively:
...it is not for me to presume to set myself up as the one person able to answer it. And so I leave it with all of you. Which came out of the opened door--the lady, or the tiger?
The story is famous because of that ambiguous ending.