In what ways is Iago considered 'Lucky'?
Iago succeeds in arousing Othello's suspicions of Desdemona's behavior with Cassio, but he has also aroused his anger. In Act 3, Scene 3, Othello demands that Iago produce proof of his wife's adultery.
If thou dost slander her and torture me,
Never pray more; abandon all remorse;
On horror's head horrors accumulate,
Do deeds to make heaven weep, all earth amazed;
For nothing canst thou to damnation add
Greater than that.
It happens that Desdemona loses a handkerchief which was a gift from Othello. Iago's wife finds it and gives it to her husband, who contrives to have Cassio find it and give it to Bianca. This bit of luck enables Iago to give Othello the "ocular proof" of his wife's infidelity he demands.
Earlier in the play Cassio had disgraced himself by getting into a drunken brawl and had lost his post as Othello's lieutenant. This was a bit of luck for Iago, because Cassio was getting Desdemona to plead with Othello to restore Cassio at a time when Othello was jealous and suspicious. Poor Desdemona didn't realize that her pleas were only adding fuel to the fire, making Iago's accusations seem more plausible.
Iago may have been too lucky. He probably didn't foresee that Othello would go so far as to murder his wife. He probably expected Othello to divorce her and send her back to Venice. But the murder brought out Emilia's revelations and accusations, leading to Iago's arrest and certain future execution.
Iago seemed to depend a lot on luck. He initially had no idea how things would turn out, but he was determined to be watchful and to take advantage of any opportunity to profit by other people's weakness or mistakes. He is an opportunist. He is also a consummate dissembler because he has everyone believing he is the soul of honesty.