Bring a large pot of lightly salted water to a boil. Cook lasagna noodles in the boiling water, stirring occasionally, until tender yet firm to the bite, about 8 minutes. Drain and pat dry with a paper towel.
Mix ricotta cheese, spinach, and half of the mozzarella cheese together in a bowl.
Preheat oven to 375 degrees F (190 degrees C).
Heat oil in a large skillet over medium heat. Add chicken breasts; cook until they turn white, 2 to 3 minutes per side. Add green bell pepper and mushrooms; cook and stir until softened, 3 to 4 minutes.
Cut chicken breasts into small pieces. Transfer to a large bowl; mix in bell pepper, mushrooms, and spaghetti sauce.
Lay 1 noodle on a flat work surface. Spread some of the ricotta cheese mixture on top. Roll up and place seam-side down in a baking dish. Repeat with remaining noodles and ricotta cheese mixture. Pour chicken and sauce mixture over noodles. Cover baking dish with aluminum foil.
Bake in the preheated oven until sauce is bubbly, about 25 minutes. Remove foil and sprinkle remaining mozzarella cheese on top. Continue baking, uncovered, until cheese is melted, about 15 minutes.