I agree that this has red flags all over it and that you'd do well to proceed with caution. Lying is definitely a problem but so is expecting the whole truth all the time. I'm not saying you are, just bringing it up to think about.

People have a right to some degree of emotional privacy and don't have disclose everything all the time. Sometimes people feel cornered by excessive questioning. (And granted if you're having affairs, emotional or otherwise it's not a great way to win trust.) Sometimes people lie because the consequences of truth-telling are too painful.

I raise this because he told you only two months in that he was in therapy and instead of thanking him for his trust and honesty in choosing to tell you, you got all upset that he lied. But if I understand correctly, this was just a temporary omission not a lie. You're angry that he told you the truth on his timeline instead of yours. If he had told you from the start that he was in therapy, would you have let him share it with you--or not--at his own pace or would you have expected a weekly report?

Not to get all Col. Jessup on you but: if you want to be told the truth, you have to show that you can handle the truth--even when it's uncomfortable, unpleasant, or overdue. If you punish the truth-teller for their disclosure, you're effectively telling them that they're better off lying. You have to make sure you're a tellable person.