Preheat oven to 350 degrees F (175 degrees C). Bring a large pot of lightly salted water to a boil. Add noodles and cook for 8 to 10 minutes or until al dente; drain.
In a small saucepan, saute onion and mushrooms in chicken broth. Remove from heat. Stir in soup, milk and basil. Mix well. Set aside.
In a lightly greased 9x13 inch baking dish, arrange 3 cooked lasagna noodles. Layer as follows: 1/2 the chicken, 1/2 the ricotta cheese, 1/2 the Cheddar cheese, 1/2 the Parmesan cheese and 1/2 the mushroom/soup mixture. Add the other 3 lasagna noodles and repeat layers. Bake uncovered in the preheated oven for approximately 50 minutes.