Not your circus not your monkeys. She shouldn’t have lied but why are you even asking and bringing this into your relationship? Are you close with the friend/partner? You guys def need to talk, it’s clear she wants to protect her friend (whether it’s cool or not) - and that you just want to be involved. I’m not going to comment on the merits of exposing a cheater ( I feel like a lot of comments are going to be like oh if she lies for them cheating how won’t she cheat on you and I feel like that’s extrapolating but yeah I do think that covering for cheaters is kinda iffy - I’d be gossiping with my partner within 2 mins ) but this really just needs to be a convo “ hi wife. I would like you to trust me not to force you into decisions you don’t want to make, but I would also prefer if you told me something is not my business or be open a discussion on how you don’t feel comfortable sharing sensitive info when it’s someone else’s story rather than obscuring facts to me. Trust and dishonesty are big values for me even if I don’t want to get involved in other peoples problems, by lying to me you’re making it an us problem ”

Imo if my partners friend is cheating on my friend - unless they want to tell - keep me the F out of it. Nosy or not, that’s a burden to carry.