Lena gets treated like a doormat and money donator by her Mom currently and some dialogue hints strongly that this has been the case for a long time. Now just think about what would happen, if Lena learns that her Mom beside treating her like an unloved add-on, also lied about who her real Dad is?Lena might not be sending any money to her mom to begin with. She certainly wasn't during all the early years after her dad left them, and her mother would need to replace those pictures pretty early on, for Lena not to remember what he looked like. Also, why would Lena learning Seymour is her dad would make her stop sending money to her mother, if she's been doing that? It doesn't make any sense.
Most people would be very pissed off and Lena hardly an exception. Many would cut off contact.