"Based on that lie" is probably a bad choice of words, but it's absolutely the case that the OP is now in a situation where his actual story is not likely to be believed. She's been explicitly shown proof that he lied to her and has been told that he's not trustworthy by the OP's brother. So that's already two strikes against him, one a very big one.

Combine that with how outlandish OP's story is, and it'll be a whole lot easier to believe that his actual story is yet another lie to try to cover up the "truth" that he really did sleep with his sister-in-law. Maybe she will believe him, or will at least be willing enough to give him the benefit of the doubt and look at any evidence he can provide. But I wouldn't be at all surprised if she doesn't believe him, because in her mind he's already provided sufficient proof that he's not trustworthy.

It's perfectly fine to not want anything to do with your past. The problem is that it would have been the easiest thing in the world to say he's not in contact with his family for personal reasons and have that be that. But as soon as she finds out that this very big thing about him is a lie, she has to start wondering what else he might have lied about, and that's probably it for the relationship.

The relationship wasn't based on the fact that his family was dead, but it likely was based, in part at least, on honesty and trust. And that may be damaged if not gone now.