I have discovered introducing a larger breed dog to the family of small dogs takes LOTS of supervision and work on my part.
We introduced a 15 week old AmStaff to our family in Feb. Ernie, our AmStaff, is
never left alone with the smaller dogs. We also enrolled Ernie in a beginner obedience class to socialize him with other dogs of all sizes. When we are not able to properly supervise the furr kids, Ernie spends time in his oversized crate which is in the living room, or he is with DH in his office during the day. Both DH and I spend time each evening will all 3 dogs together. With gentle correction, Ernie has done remarkable with learning how to play with the girls. We taught him to lay down when they approach him so that he is on their playing ground. His huge paws are my biggest fear right now, they will rare-up at him and he will swat with his paw that is about the size of their face.
You just have to remember that these large breeds are really just BIG puppies at this stage and can really hurt their small buddies without meaning to. Ernie is full of energy and LOVES to play. We usually take him outside each evening alone and play fetch, keep-a-way or other games for a while so that he can use up some of his energy before playing with his 10 lb playmates.
With lots of work and patience on you part, I am sure Lilly will become a wonderful playmate for Lilly. Good Luck and Welcome to YT!