Poetic justice is that idea that a person gets what he or she deserves by the intervention of fate. In other words, the justice is not meted out by people. It comes naturally.
Lady Macbeth is really the impetus for all of the destruction in the play, in a way. The witches tell Macbeth that he will be king. When Duncan names Malcolm his successor, without waiting to see if he will be she automatically decides that killing Duncan is the only way. This created a turn of events where she spurred Macbeth on each time he was having doubts.
If we should fail?
But screw your courage to the sticking-place,
And we'll not fail. When Duncan is asleep—
Whereto the rather shall his day's hard journey(70)
Soundly invite him—his two chamberlains
Will I with wine and wassail so convince,
That memory, the warder of the brain,
Shall be a fume and the receipt of reason (Act I, Scene 7)
Lady Macbeth is not afraid, at first, although she does point out that she couldn’t kill Duncan herself because he looked like her father. She says that the blood will wash away easily. This foreshadows her descent into madness.
Out, damned spot! Out, I say! One–two—
why then ’tis time to do't. Hell is murky. Fie, my lord, fie! (Act 5, Scene 1)
Did she deserve it? Macbeth doesn’t think so. He clearly feels bad when he finds out.
She should have died hereafter;
There would have been a time for such a word.(Act 5, Scene 5)
Malcolm suggests that it is indeed deserved.
Of this dead butcher and his fiend-like queen,
Who, as ’tis thought, by self and violent hands(80)
Took off her life; (Act 5, Scene 8)
Lady Macbeth’s sins carried their own punishments. She did not have the mental strength for murder. Neither did Macbeth. Did she deserve to die? Perhaps. That is not for us to decide. Was her death at her hand poetic justice? Yes it was. She punished herself.