Sophia is going to a lot of effort and risk to educate these 3. If LP continues this "I'm doing this for education purposes only, it makes no sense" Sophia is doing it, given the risk and effort, because she wants to.
As for the lingerie, she could have just worn it under her clothes. The bag contains a dildo. No other plausible explanation. And it looks weighted down. And will make a sizable noise when tossed up to the balcony. And when the daughter comes out to see the noise will discover a bag with a vibrating dong inside and Sophia looking embarrassed down on the grass. And thus...lesbian encounter.