"The Lady, or the Tiger?" uses dramatic irony. Dramatic irony occurs when the character, usually the protagonist, does not understand or know some critical truth, but the audience or reader fully understands the entire situation. Dramatic irony creates a discrepancy in perspective; for the moment, the audience or reader knows more than the character actually in the story. In "The Lady, or the Tiger?" dramatic irony unfolds as the hero steps out into the arena, and the narrator reveals that the princess knows the secret of the doors, and not only that, but she cannot decide whether she should let the tiger eat him or allow him to be married to her much hated rival.
Situational irony also occurs as the hero willingly trusts the princess' direction on which door to choose. His unwavering faith in her is a sharp contrast to her debate on whether or not she would rather see him dead or alive and married.
Situation irony occurs when a situation arises and the opposite of what we, the audience, expect to happen arises.
Verbal Irony, is when we say one thing and mean another.
The King's method of "semi-barbaric justice" is a perfect example of this verbal irony, since we do not expect a barbaric person to understand the civilized notion of justice.
On the same note, it is situation irony that the king has built a stadium for his justice, and if the person is found guilty by chosing the door with the tiger in it, they are automatically found guilty (regardless of their true guilt and innocence) and immediately given a state funeral. If they choose the correct door, independent of innocent or guilt, they are immediate declared innocent, and given to marriage (whether they want to be or not).
Another bit of situation irony is that the princess used means to discover what no one else was able to, the location of the tiger on the day her lover would be put to judgement. However, she is so internally conflicted, her good intentions are put on the back burner.