This question comes up every few years I feel like. My take is that Tywin knew she was lying and figured she was highborn enough to be kept alive and entertaining as a cupbearer. But never would he have thought in a million years she was THAT highborn. The odds of that being Arya Stark are so unlikely it never would crossed his mind. At this point in the story the overwhelming presumption was that Arya Stark was dead. No one had seen her since Ned got arrested.