I would recommend just telling him that you've realised you don't want to date him again and have decided to move on. And if he asks why, just say that you have moved on.

You don't have to say what you found, you don't have to say anything, he doesn't need a specific reason, because deciding to move on is a reason.

It didn't work, you don't want to try again. Done.

But if you don't tell him something, he's going to keep trying. I think it's kinder to both of you, to say something. Over message is fine, you don't need to call or anything, and you don't need to block or be unkind or whatever. You've decided to move on.

Cheaters need to want to change. And if he's lying to you, he doesn't want to change.

Does the service account for when tinder was used last?

For instance, I just checked, and I never deleted my profile from over 6 years ago, I just deleted the app. I've done so now, but just wanting to make sure you're not recommending an app to people that doesn't account for that.

Either way, if you're at a point of needing to check that, the relationship is already over, because trust is totally gone. If he's been lying to you for a long time now, then it's best to be gone as well.