The three major types of conflict that shape storytelling are generally man versus man, man versus self, and man versus society. "The Lady, or the Tiger?" contains examples of all three types.
This story's use of man-versus-man conflict is centered around its king, who orders the youth to undergo this trial, with chance dictating whether he will be found guilty (and killed by the tiger) or found innocent (and married). The king is clearly the villain of the piece.
Meanwhile, the story's use of man versus society can be observed perhaps most strongly in the romance between the youth and the princess. They love one another intensely, but theirs is a forbidden relationship, one that must be pursued in secret, and as soon as it is discovered, the youth is forced into the trial.
The last, and (within the context of the story) most vital conflict is internalized, existing within the mind of the princess herself. As the story reveals to us, the princess has managed to discern which of the doors holds the tiger and which the lady, and she furthermore has the ability to signal to the youth which one he should pick. However, this raises the story's critical dilemma: is she is willing to save her beloved if it means giving him up? It is this internalized conflict, in which her love for the youth is weighed against her feelings of jealousy and resentment, that shapes the story's thematic architecture and the cliffhanger on which it ends.