Disgrace chapters 10-14

At the start of the reading I thought that David was going to leave Lucy and return to the city for a faster pace life.  When David was working at the clinic it didn't seem as he was much help to Bev. When David returns home he finds Lucy on the phone and starts to ponder her love life.  When David and Lucy go on a walk they pass three creepy men that just keep going when they return to the house they are at the dog cage and create a story about why they need to use the phone.  Did these three men know that Lucy lived alone and she would be an easy target, but they had to handle David?  I think the goat from the clinic foreshadowing what was going to happen to David.  The next day David is taken to the hospital  to have his wounds check out and they are much better then I assumed they would be from being set on fire.  David keeps pushing Lucy for answers about what happen to her and why she won't tell the police about the rape.  She says it is about a private knowledge in Women in America private knowledge is only between women and whats goes on in the family, is this the same concept?  Also does Petrius have anything to do with the attack because he won't fess up about his location.