The speech of Lennox in this scene is important because it shows how the pretence of Macbeth is under great suspicion. Note the sarcasm with which Lennox comments upon how conveniently it has all worked out for Macbeth, especially with regard to his "noble" act in killing Duncan's henchman who supposedly killed Duncan:
How it did grieve Macbeth! did he not straight,
In pious rage, the two delinquents tear,
That were the slaves of drink, and thralls of sleep?
Was not that nobly done? Ay, and wisely too;
For 'twould have anger'd any heart alive
To hear the men deny't.
His speech is of course an example of dramatic irony, for he is only able to suspect what we as the audience know: that each one of his suspicions is actually true, and that Macbeth is a cold-hearted murderer and a tyrant. This scene is important as it shows the way that Macbeth's behaviour is eroding his support in Scotland, and alienating the nobles from him, not just Macduff. This in turn foreshadows the desertion of his forces in the final act when he is left to face Macduff alone.
Another way in which Lennox's speech can serve as an example of dramatic irony is in the dramatic change that has taken place in this young man's character since he first appeared with Macduff when they came to wake King Duncan. At that time Lennox was young, callow, naive, awkward, self-conscious, and inexperienced, just starting off in life as a soldier and a courtier. By the time he makes the speech in Act 3, scene 6, the events he has witnessed and the things he has personally experienced have made him grow up very quickly. Now he is cynical, embittered, worldly wise, and cautious. At one point he says:
But, peace! For from broad words, and ’cause he [Banquo] fail'd
His presence at the tyrant's feast...
If a young man like Lennox can have changed so much and come to such conclusions as he expresses in this speech, it is a strong indication that many other people, nobles as well as commoners, have done likewise. Lennox is a spokesman for the general animosity and unrest which will lead to Macbeth's downfall.
It is, in fact, Lennox's sarcasm that sustains the dramatic irony. The audience knows that Macbeth is guilty, and subsequently that Fleance and Duncan's sons are innocent. Dramatic irony occurs when the audience knows something that the characters do not. In this play, no one (other than Macbeth and his wife) initially know the truth of Duncan's murder. Eventually, others such as Malcolm and Macduff become suspicious of Macbeth.
This scene is interesting because of the language and the sarcasm. Lennox is stating what happened and he does so bluntly. Read without sarcasm, it would seem that Lennox has no idea that Macbeth had some role in the murders; thus, Lennox is still in the dark and the dramatic irony continues. However, read with sarcasm, the dramatic irony is broken (at least with Lennox) because he is starting to presume to know what the audience has all along: that Macbeth is behind all the murders. By the end of the scene, Lennox is no longer sarcastic and has become completely direct, siding with Malcolm in England and opposing Macbeth's "hand accursed" at home in Scotland:
Fly to the court of England and unfold
His message ere he come, that a swift blessing
May soon return to this our suffering country
Under a hand accursed! (III.vi.49-52)