In a medium frypan saute the chopped onions, celery and garlic in oil until soft and tender. Add chopped turkey and broccoli. Set aside.
To make white sauce: In a small saucepan over low heat melt butter or margarine. Remove from heat and add flour, salt and pepper; and blend well. Return to low heat, whisk in milk and cook until thick.
To assemble, in the bottom of a casserole dish place a thin layer of white sauce, then a layer of lasagne. Next, place a layer of the turkey mixture, followed by sauce and then 1/2 cup of the grated mozzarella cheese. Repeat layering process with lasagne, turkey mixture and sauce. Top with the remaining 1/2 cup of mozzarella cheese.
Bake in a preheated 180 degree C oven for 45-60 minutes until bubbly and heated through. Let stand 10 to 15 minutes before serving.