What is the purpose of act 3, scene 6 of Macbeth?
By this point, Macbeth has killed Duncan, his two guards, and Banquo. He also acted strangely at a banquet where he saw Banquo’s ghost, when he all but admitted to his crimes. In Act III, Scene VI, Lennox ponders over Macbeth’s behavior: “Things have been strangely borne.” He first points out how Macbeth cared for King Duncan, yet he is dead. Macbeth’s friend Banquo was also killed, perhaps by his son Fleance. If taken at face value, they are to believe that both Duncan and Banquo were killed by their own sons, which is “monstrous” and unusual.
Lennox does not outright say that he suspects Macbeth, perhaps for fear of being overheard. Instead, he praises Macbeth’s behavior, noting how the king’s death “did grieve Macbeth” and how he “nobly” and “wisely” killed the two men who seemed to have committed the murder. However, the other Lord refers to the country’s leader as a “tyrant.” He relates the plan to gather Macduff, Malcolm, and other lords in order to challenge the current king. This all foreshadows Macbeth’s downfall at the hands of an army and Macduff himself. The scene is small, but it signals shifting loyalty amongst Macbeth’s acquaintances and friends and their awareness that their “suffering country” is “Under a hand accursed!”
With all due respect to tthakkar, Macbeth was actually performed for King James I. This play would have had some special significance to King James as he was one of those descendants of Banquo - the line of kings shown in the mirror during the witches' prophecies.
This show of respect to King James from Shakespeare is why it was so easy for the king to commission Shakespeare's troupe as "The King's Men."
In this scene, Lennox hints at his belief that Macbeth is responsible for the deaths of the king and Banquo. The purpose is to let the audience know that Macbeth's people do not trust him, foreshadowing his eventual downfall.