When a parent lies about the father

[Milsplus3]

I’m posting for a friend who needs advice and I’m not sure how I can help her so hopefully someone here has the experience or advice for her I can pass on.
She is in her 20s and was raised by a single mum who told her that she didn’t know her father. He had been a one night stand who gave her a fake name and was actually married etc etc so she couldn’t trace him to tell him he had a daughter.
Well, her mother and aunt were discussing exes and her mother accidentally let slip in front of her she did know her father all along, that he had given a real name and was actually traceable but she didn’t want him to be involved so she lied that my friend wasn’t his baby.
She’s obviously upset and wants to find her father but many people are telling her to drop it as it could open a can of worms and hurt the father and his family.
What would you do/say?

Call my mum a lying bitch probably.

I think your friend is entitled to follow this up. If it opens up a can of worms, that's not her fault.

The question may be whether her mother is prepared to reveal the identity. And I suppose also which story is true - the whole 'used fake name but mysteriously was definitely married' thing doesn't even make sense. Is it possible the mum is lying now as well?

It’s very possible she’s also lying about that but she must know something to have brought it up 28 years later