I think having Lucy ask for help would be a good cause of action. I'm not sure how we handle this in-game though, because they are way ahead in their thread, the house thread is still hours behind XD
What time is it currently in the girls thread approximately? I wonder if Jerome would write Lucy before she posts on the network, because he is about to discover the message on the ground, and he is already worried about Lucy, but after seeing that message he will be REALLY worried about Lucy.