What lies does Iago tell in the play Othello?
Gosh, it would be easier to try to recall the times he told the truth—that's how often Iago lies in the play.
In general, though, there are lies of character and actual spoken lies. The lies of character are that he presents himself as someone who is on the side of Othello, Brabantio, Roderigo, Desdemona, Cassio, Emily…and he's not, ever. He's on his own side, the side of revenge.
As far as specific lies, he lies to Brabantio about Othello having stolen Desdemona's love (they did elope, but Othello did nothing else wrong), and about Othello currently having sex with Desdemona, even as they speak. He lies to Othello about where the handkerchief came from. He lies to Othello about what he overheard Cassio say about Desdemona, and about often seeing them together. He lies to Roderigo about Desdemona loving Cassio, etc.
Iago's character works as a foil to Othello. His character dominates the first part of the play. His main purpose is getting Othello to see the world through his eyes.
One of the main lies, and one of the most important, is one that he tells himself. He convinces himself that Othello has had an affair with his wife.
Iago also lies to Othello when he tells him that Cassio is having an affair with Desdemona. He gets Othello to "turn" at this point and then Othello becomes driven to kill his wife.
In these and other ways, Iago exploits opportunities in order to bring the downfall of all of those who "hath a daily beauty in...life that makes [Iago] ugly."
The best way to seek out Iago's lies, it to focus on what he says he motives are. These motives can be found in each soliloquy, which, in turn, forwards the plot of the play. Iago begins the play with lying about Cassio's capabilities, but he thens continues to lie as he tries to hunt for motives to justify his evil actions. Focusing on each soliloquy and the inconsistencies with which he justifies his actions will give you the key to his lies.