Would you let it go or no?

Been with my boyfriend for what is now two years we moved in together beginning of this year. He was in a long relationship for three years before me and I was helping him recover his old email and his old search history popped up a lot had to do with her while dating her, and he lied about tons of shit about their relationship. Another thing is he said he never saw this one girl in person or hung with her yet she was able to describe his whole house but this was years ago. He’s still denying it. He denies a lot about his past. I know its his past and everyone has one. But what if he’s a liar and lying about EVERYTHING? He’s super loyal with other girls he literally doesn’t even have girls in his phone and him cheating on me is like not even in my worries. It’s just the lying. I feel like if he can lie about the past he’ll lie about everything. He swears on everything in the world even his dying grandma that he’s not lying. What would you do? I can’t let it go it’s causing our relationship to crash but bringing it up everyday isn’t doing us no good. What would you do? Let it go because it was like 4 years ago, or leave? Advice.