Kirsten, I wonder what goes on during the day. Could you use a tape recorder and see if there is anything?
I was often wondering about this myself! I could try to set up my old webcam, it would be interesting to see what they are doing when I'm not at home!

When Lilly stalks, and you intervene, you are "rewarding" her with attention- your attention. How do you break things up? Clap? Use some other sound device? Do you go to Luna, and comfort her?
Well, so far, I avoided to interfere, I don't want any of them to feel I'm taking sides. I always thought they should work out their problems on their own. But during the last couple of days, when I felt too sorry for Luna, I caught myself that I comforted her, and tried to encourage her. But I always ignored Lily when she acted like that, I didn't want to give her any attention for this behavior...

Kirsten