It will return long after he earns it. He needs to demonstrate consistently, over a long period of time, that he is dealing with you truthfully. Once you've lived with that, you'll begin to internalize it and trust him again.
You need to make sure he sees this as a big deal right now. It sounds like you caught him in the same lie before, he said, 'oh, okay, it's nothing, and I'll stop if you want' but then went back to it. It was a lie by omission, maybe he could try to play dumb. Now it's a to-your-face lie.
He needs to do a no contact letter and stand by it. He needs to be very transparent with you- you need full access to his phone at all times, and to know where he is and who he is with at all times. You don't trust him, and have good reason not to.
Then, while you may not want to talk about it all the time, you need to talk about it. Find out what it was, how long it was, how it started, how he rationalized it, how he is going to do something else in the future. Get the books. Get into counseling. This is really happening, and it really is a big deal. If he can't face the music, he isn't about to change his behavior.