In "The Lady or the Tiger," of what crime is the young man accused?
Looking at the story carefully, we see that the "crime" that the young man was accused of was actually loving the daughter of the king. It was only the discovery of the relationship between the daughter of the king and the young man that brought about this accusation. For us, this "crime" seems rather unfair as it is not actually a crime, but the text is careful to tell us why this was regarded as a crime in this particular time:
Never before had such a case occurred; never before had a subject dared to love the daughter of a king. In after-years such things became commonplace enough; but then they were, in no slight degree, novel and startling.
Thus, from this quote, the precise nature of the crime that the young man is accused of is falling in love with somebody that was regarded as socially being his superior. We can see from the quote that "daring" to love the daughter of the ruler was an unheard of event, and was regarded as a crime because persumably the king was the one to decide who would marry his daughter.
As is often the case in fairy-tale-like stories, the crime of the young man is daring to fall in love with a princess, "the daughter of a king." The assumption is that, at this time long ago in this mythical kingdom, a strict class hierarchy is in place, and the young man, apparently without any title, such as lord or earl, is breaking the law and out of line in even looking at a princess in a way that might communicate love to her.
The fact that he is put on trial carries with it a presumption of possible innocence. In this case, however, each possible outcome works out in favor of the king and against the interests of the daughter. If the young man opens the door with the tiger behind it, he will be devoured. If he opens the door with the maiden behind it, he will marry someone other than the princess. For the king this is win-win, for the daughter lose-lose. The only one in a win-lose situation is the young man.