My (20f) new Girlfriend (21f) claims my dad (who she randomly met) told I her was cheating after I asked for some space. I asked for space because my dad died on March first. How do I confront her?

I don't even know how to start. English is not my native language, so please excuse any mistakes.

Me (20f) and Anna(21f, fake Name) started dating Valentines Day this year after meeting randomly at my place of work and getting to know each other. Our relationship is relativly new. We also all (my family, Anna, and me) online in the same city.

Like you can see from the Title, my dad passed away unexpectedly March first. Anna doesn't know that he died. She only ever saw pictures of my family and hasn't met them in person yet. Likewise, my family knows about her and has seen pictures of her, which she is aware of. ( I told her my whole family thought she was pretty after I showed them a picture of her)

I didn't want to tell her because I had a complicated relationship with my dad, and our relationship is so new that I didnt know how to bring it up. I'm still having trouble talking about it with friends and family, I have no Idea how to tell my (new) girlfriend. So I told her that I needed some space and time for me because of "personal Problems". Obviously I was still planing on telling her, just not right now. It's all a bit much.

She knows how my Dad looks like because I showed her pictures of a family vacation from last december. She claims that last Friday, she and my Dad met in the grocery store. He came up to her and "warned" her about me. That I was boasting at Home that I had multiple relationships so that "it never got boring". That my personal Problems were an excuse to spend time with other women. She wants to meet this evening to "talk it out" and "see if she can forgive me".

Obviously I know she is lying. But what the f*** am I supposed to say that? I know you're lying because my dad is dead? Why would she even do something like that? For all she knows my parents could be on vacation right now. Or I could have gone no contact since I last saw them.

Why would she lie about that? I also need advise on what on Earth to say to her. I definitivly don't want to continue the relationship, but I also don't want to ghost her because I want to know what caused her to lie. I know she couldn't have known he had died (we're trying to keep it Private) but it still makes me angry that she involved him in her lie.

TLDR: My Dad died unexpectidly March first. My new girlfriend claims she randomly met him in the city we all live in, were he told her (after recognizing each other from pictures) that I was cheating on her after I asked for some space. She wants to meet this evening to talk it over, but what am I supposed to say to her?

Edit: I am supposed to get ready to meet her now. However after reading all your comments I decided not to go. You all are right, I can gain nothing from this. I send her a picture of his death certificate and blocked her. I hope that was the last of it. I still want to know why she lied, but I doubt she is going to be honest with me. For everyone asking why I didnt tell her: I don't know. He died unexpectidly in the middle of the night. I had dinner with my parents the Night before and everything was still fine. The next day he was dead. I didn't know how to react. Something like this obviously never happend to me before. I just wanted space and time to grieve on my own.

Edit2: Thank you for your condolences. I stopped responding to comments (there are simply to many) bit I still read them all. I would like to clear some things up:

1.I'm a woman as well. Part of my difficult relationship with my dad came from the fact that he only recently startet accepting me.I came out at 18, he only started accepting it (and me) back at the beginning of last year.

1. I'm from germany. I don't know how it works in the US, but here the motician takes care of getting the death certificate for you (if you want). It only took 3 days before I got it.

2. We (Anna and I) don't work at the same company. We met at my place of work, she was just a regular customer.

3. Anna absolutly insisted it was 100% my dad. I don't know what her endgoal was, or how she thought it would play out. But I don't know why someone would go up to her and pretend to be my dad. I already said it in a comment, but he has a pretty noticeable and unique scar on his face from a car accident when he was younger. The chance that some random person who looked like him had the same scar is pretty slim in my opinion.