Lady Macbeth is rational because she wants her husband to be king because it will increase her status. She is irrational because she wants him to do it by murdering Duncan.
Sometimes rationality is in the eye of the beholder. Both Macbeth and his wife seem to think that because the witches said he would get a promotion to Thane of Cawdor and then be king, that this must happen. However, it is irrational to assume that because a witch tells you something it will come true. Although it is perfectly rational and normal to want to be queen, it is not rational to decide to kill the sitting king so you can be queen.
There are some rational elements of Lady Macbeth’s plan. It is well thought-out.
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 … (Act 1, Scene 7, enotes etext p. 24)
She tells her husband to invite Duncan over, be nice to him, and then kill him in his sleep. Other parts of the plan involve getting the guards drunk and framing them for murder by leaving the daggers next to them. This will implicate Duncan’s sons, thus clearing the way for Macbeth to be king.
Why did you bring these daggers from the place?
They must lie there. Go carry them, and smear
The sleepy grooms with blood. (Act 2, Scene 2, p. 30)
It is a very rational plan. After Macbeth kills Duncan, he is made king. The sons, Malcolm and Donalbain, are suspected and flee. Everything falls into place.
It was irrational, perhaps, for Lady Macbeth to assume that her husband would leave it at that. As the death toll rises, Lady Macbeth loses her sanity. She begins sleepwalking, trying to get the blood off her hands.
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, p. 77)\
Eventually, she completely loses it and kills herself. Lady Macbeth’s grasp on rationality is gone, and she can no longer live with the guilt of what her husband has become and her part in it.