Preheat oven to 400 degrees.
Spread a thin layer of bolognese sauce on the bottom of a 9x13 casserole dish.
Arrange lasagna noodles in a single layer over the sauce. It's okay if they overlap a bit. Break the noodles as necessary to cover the bottom of the baking dish.
Spread a layer of bechamel sauce over the noodles, followed by a layer of bolognese sauce and 1/4 of the Parmesan cheese.
Repeat this pattern two more times: noodles, bechamel, bolognese, 1/4 cup of Parmesan cheese.
Finish with a final layer of noodles. Spread the remaining bolognese sauce over the noodles. Sprinkle the grated mozzarella on top.
Cover with aluminum foil. Bake 45-50 minutes. Remove the foil and bake another 10 minutes. Allow the lasagne to rest for 15-20 minutes before cutting into it.