I have adopted many cats into my house and I have found that when I have done this my cats have always reacted in the way that Toby is reacting. They would either bite each other, chase each other around the house, or would have a wrestling match with each other. They are just getting the "pecking order" so to speak. Toby has been your only baby for a while and now you have Lily. In my opinion he is just letting Lily know that he was here before her.

Many people may disagree with this but it is what I have done and it seems to have worked. When we have outbreaks in our house I use a water gun to get them to stop. It usually takes a little time. We still have outbursts in the house from time to time, but otherwise they (all 5 of them) co-exhist very well.

I hope this helps.

P.S. Toby and Lily and so beautiful. I have been enjoying the pictures that you posted.