What evidence is there in Act 3 Scene 6 that Lennox in convinced that Macbeth was responsible for the Murder of King Duncan?
Lennox's speech is filled with verbal irony. Even though he does not state his suspicions directly, it is clear that he is sarcastically blaming Macbeth for the recent murders. For example, he says,
The gracious Duncan
Was pittied of Macbeth; marry, he was dead.
And the right-valiant Banquo walked too late;
Whom you may say, if 't please you, Fleance killed,
For Fleance fled.
By tying the two murders together--Duncan's and Banquo's, Lennox is suggesting that anyone who gains Macbeth's sympathies suddenly finds himself dead. He preposterously places the blame for Banquo's death on his son Fleance, just as Malcolm and Donalbain were blamed for Duncan's death because they ran. Just as Fleance's escape did not mean that he killed his father, Malcolm and Donalbain's fleeing Scotland does not mean that they killed Duncan.
He goes on to seemingly praise Macbeth for "nobly" killing the guards because they would have most assuredly denied killing Duncan. Of course, they would have denied killing Duncan--they were innocent. He then comments that if Macbeth were able to capture Malcolm, Donalbain, and Fleance, they would all be put to death for supposedly killing their fathers.
In this fashion, Lennox shows that Macbeth is the culprit in the murders of Duncan and Banquo and that he attempted to place suspicion on others who fled or whom he killed. At the end of this speech he calls Macbeth a "tyrant," and at the end of this scene, Lennox hopes that Scotland will find relief from its suffering "under a hand accursed."