I drink tea with milk all the time and Im never out of ketosis, I must admit Ive not really done an induction, Ive kind of made mine up as I go along but have followed the basic rules, the main reason I didnt do the induction was because I had lost 20 pounds in the 2 weeks prior to going onto the Atkins diet with LL and was in ketosis, I know I could lose more weight if I was slightly stricter but to be honest I think the most important thing is to find a way to eat that you feel comfortable with and accept that losing 2-3 pounds per week is fantastic when you feel good doing it, from your diet you posted I can't see anything wrong with what you are eating, so I guess it is just a matter of time until it starts to work for you, also I am interested to know how you feel apart from the fact of putting on the 4 pounds and if you weighed yourself at the same time in the day both times.