What are three examples of irony in "The Lady, or the Tiger?"

I think that you are probably looking for examples of
verbal irony here.  This is the type of irony where the author says one thing, but
really means the opposite.  There is quite a bit of this in the
story.

Here are a few examples from the
story.

First, the narrator says that the king
made

the
public arena, in which, by exhibitions of manly and beastly valor, the minds of his
subjects were refined and
cultured

This is ironic
because the minds of his subjects weren't really being cultured by this -- it's
barbaric.

Second, we are told
that

The arena
of the king was built, not to give the people an opportunity of hearing the rhapsodies
of dying gladiators...

Dying
people don't do rhapsodies.  So that's ironic too.

Finally,
the narrator says this about the method that the king made up of deciding whether
someone was innocent or guilty:

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Its perfect fairness is
obvious.

This is ironic
because the process was ridiculously unfair and
arbitrary.