In reference to Macbeth, what would it mean for the play if Lady Macbeth were the third murderer in Act III?
Since Lady Macbeth is not identified as the third murderer in Shakespeare's Macbeth, and since the only way she could be the third murderer is to be portrayed as such by a production of the play, and since Lady Macbeth being the third murderer makes no logical sense, it would mean that some director and actors took some silly liberties in interpreting the play.
Or, if you're asking what it would have done for the play had Shakespeare written in Lady Macbeth as the third murderer, the answer to that is that it would show Shakespeare isn't as good as we think he is.
You see, Lady Macbeth can't even kill the king, because the sleeping Duncan reminds her of her father. If she can't kill Duncan, she certainly isn't going to attempt to kill Fleance. Plus, by this time in the play Lady Macbeth has been shut out of the decision-making process. She doesn't even appear to know about the murders until after they occur.
Finally, Lady Macbeth makes plans that work. She is the planner of the family. Duncan's assassination comes off with no problems, until Macbeth varies the plan and kills the grooms. The plan to kill Banquo and Fleance fails, and the plan was ill advised in the first place. Lady Macbeth would not have devised this plan.
This is a really interesting question. If Lady Macbeth had been the third murderer, her participation in Banquo's murder and the attack on Fleance would have added new elements of deception to the play. Macbeth ordered the murders of Banquo and Fleance independently; he acted on his own, without taking his wife into his confidence. If she had learned of the plot and participated in it, it would have been without Macbeth's knowledge. She then would have been keeping her own secret from her husband. When Banquo's ghost appears at the banquet, Lady Mabeth's conduct would have been another deception, since she shows no knowledge of Banquo's murder.
Also, if Lady Macbeth had been the third murderer, her participation would have further developed her character as a woman of action, one who takes charge of events and situations. Just as she engineered Duncan's murder, she would have acted to take Banquo's and Fleance's murders into her own hands.