If Macbeth is a protagonist, what is Lady Macbeth? Is she a protagonist as well, or is she an antagonist?

The difference between Macbeth and lady Macbeth is lady Macbeth is active while Macbeth is imaginative and thoughtful. Her ambitious nature instigated her husband into action. This is too for the sake of her husband. Her strength of power and action should be highlighted for a woman's courageous nature. So she can also be said as the protagonist of the play Macbeth.

The term "protagonist" is taken from ancient Greek drama and simply means "first actor." The "protagonist" of a drama is the central or leading character, and he or she usually has the most lines and is played by the "starring" actor. In antiquity, the cast for a play consisted of three actors and a chorus. As well as a "protagonist," there was a "deuteragonist" (second actor) and "tritagonoist" (third actor). In some cases, a protagonist would have a strong single opponent called an "antagonist," usually played by the second actor or deuteragonist, but not all plays had that structure.
Shakespeare's Macbeth is a modern drama with more than three actors. Although Macbeth is definitely the leading role and Lady Macbeth is the second most important role (one that would have been played by the deuteragonist in antiquity), she is not an antagonist to her husband. Instead, there are a series of antagonists, including Duncan, Banquo, and, the most important, Macduff.