Melt butter in a saucepan over medium-high heat. Whisk in flour and cook for 2-3 minutes to form a roux.
Gradually whisk in milk until smooth. Add cream cheese, Parmesan, and Caesar dressing, stirring until the sauce is creamy and smooth.
Cook lasagna noodles according to package directions. Drain and set aside.
Stir the shredded chicken into the creamy Caesar sauce. Season with salt and pepper to taste.
Preheat oven to 375°F (190°C). Grease a 9x13 inch baking dish.
Layer 3 noodles in the prepared baking dish.
Spread half the chicken mixture over the noodles, followed by 1 cup of mozzarella cheese.
Repeat the layering process twice more, ending with noodles and the remaining cheese.
Cover the dish tightly with greased foil and bake for 30 minutes.
Remove foil and bake for another 5-10 minutes until the cheese is golden brown and bubbly.
Let the lasagna stand for 10 minutes before cutting and serving.