Hmmm....interesting one. I'm having to really think about what I would do here!!
On the one hand - personal tragedy aside - no one owes anyone a donation. Everyone has their cause. That said, I have never NOT donated to a close friend who is raising money for something I know matters to them. Even if it's just a fiver, it's more a gesture of how you love your friend, not the cause, right?
She shouldn't have lied about donating (IF she did) but we have all been in a situation where we have accidentally exaggerated/downplayed something and then you look back and are mortified. She likely went home and googled "can someone running a fundraiser see anonymous donators" or similar and now feels awful!
You should not have publicly queried it. I suspect you did it automatically - like how she possibly fibbed - but that wasn't cool. I think I would have done the same as you and then also felt pretty bad afterwards.
If it was a really, really good friend, who you are really close to I think I would have to discuss it or it would annoy me and fester. Plus there may be a genuine error here. So, on balance, I would approach her with kindness, and say something like:
"Hiya friend, you mentioned the other day that you donated anonymously, but I can see the names of anonymous donators and you aren't there. For what it's worth I absolutely do NOT want you to feel compelled to donate, but I'm also worried you've sent money to someone who isn't me. Just wanted to let you know so you could check! Equally if you just felt under pressure the other day in the conversation I 100% get it (and would probably have said the same)!"
Yep, it's a bit pass agg, but it's also a blunt instrument way to open up a conversation. But ONLY if you two are genuinely close and will be able to laugh about it. If not, just leave it.
I know LOADS of people are going to disagree with me on this, and the wise advice would probably be to drop it, but for me that would create a bit of a weird crack in a friendship and I'm a believer in confronting stuff head on so you have all the information. Only you know the dynamic of the friendship and whether you can be this blunt. With my best mates we could - we would discuss and ultimately laugh - but every friendship is different.
Good luck.