Combine processed cheese food and diced tomatoes and green chiles in a saucepan over medium heat; cook and stir until cheese dip is smooth, about 5 minutes.
Spread a layer of cheese dip in the bottom of a 9x13-inch baking dish; top with a layer of lasagna noodles and chili. Continue layering with remaining cheese dip, noodles, and chili. Top the final layer with Cheddar cheese. Cover dish with aluminum foil.
Bake in the preheated oven for 15 minutes; remove foil and continue baking until Cheddar cheese is bubbling and melted, about 15 minutes more. Let stand for 10 minutes.