For the sauce: In a large stockpot, combine the alfredo sauce, diced tomatoes, sun-dried tomatoes, bell pepper, onion, garlic, water, Italian seasoning, salt and pepper. Bring to a boil, then reduce heat, cover and simmer for 1 hour.
Crumble the ground chicken in a saucepan. Cook until no pink remains. Add the chicken to the stockpot. Simmer for another 15 minutes.
Meanwhile, cook the lasagna noodles according to package directions. Drain and set aside.
Cook the mashed potatoes according to package directions. Stir in butter and sour cream.
Heat oven to 350 degrees.
To assemble, place a thin layer of sauce in the bottom of a 9x13" baking pan. Layer 1/3 of each, noodles, potatoes, Mozarella, Swiss and Cheddar cheeses. Crumble small pieces of goat cheese and dot over other cheeses. Add another layer of sauce. Repeat layers 2 more times, ending with cheeses. Bake for 35 to 40 minutes or until cheese is melted and bubbly.