[Rob!]

If the last thing Lucy heard was the music box, that means she was killed in the Beale house, which means Cindy would have been there looking after the baby or whatever. Argument (in fact I wouldn't be surprised if the music box is the murder weapon). Jane comes home, and they dump her at the common.
Remember Emma going all wtf when she worked it out? "It's missing" I reckon it was Jane's car, because she was thinking about when they did that video of fats and they saw Lauren going in the house. Jane backs up Lauren saying she saw Lauren out of Massod's window, but her car isn't in the video.