Lying is almost always a product of someone not believing that the truth will be accepted (not condoning lying).
The best way to get to the bottom of it, in my experience, is to identify what is making them feel unsafe in being open and honest. It could be in their head-but usually it's an action, word or expression that they regularly get in response to unappreciated information.
You want a closed V or triad-in this case-with that piece of trivia-no this won't work. Because it isn't fulfilling one partners needs-hers.
It might work with someone. But not her.
IF you want to remain with her-then you need to let go of the "closed V/triad" because THAT dynamic doesn't allow her to get all of her needs met.
*of course that's all arbitrary if you can't resolve the trust issues that promote her lying to you AND the trust issues caused by her lying to you.
"Love As Thou Wilt"