The One With Joey's Bag - S5-E13
Corrected entry: When Phoebe is talking to her dad in the coffee house, she asks Frank Sr. about his marriage to Lily and their two children. But Phoebe has already found out that Lily isn't her real mother because she lives in Montauk. Frank Sr. would surely know that Lily wasn't there real mother if indeed she wasn't.
Correction: Phoebe's real mother left her children when they were born, in Phoebe's eyes Lily is her real mother. And Frank doesn't known that Phoebe found out about her birth mother, the easiest way for Phoebe to get information from him is to go along with the story she's been told from birth.
He doesn't know that this is Phoebe yet so he would probably correct her.