In a saucepan, melt 4 tablespoons of butter. Add 4 tablespoons flour, and stir constantly until bubbly and thick.
Slowly add 2 cups of milk (in 1/2 cup portions). Stirring and waiting till it thickens after each addition.
Set white sauce aside.
Chop all veggies.
Add 1 tablespoon of oil to a skillet and turn on heat to medium. Add veggies to skillet and cook till just under done, about 5 minutes. Set veggies aside.
Combine 1 1/2 cup mozzarella cheese with 2 cups cottage cheese and 1/4 cup parmesan cheese. Mix an egg and salt into mixture.
Prepare a 9X13 pan by spraying the bottom with cooking spray. Add 1/2 cup white sauce to bottom. Arrange noodle on top of white sauce so the noodles fill the pan. It's OK if they overlap.
Add 1/2 of the veggies to the top of the noodles, 1/2 of the cheese mixture, and 1/2 of the remaining white sauce. Repeat layers once. Top with 2 ounces shredded mozzarella and 1 ounce grated parmesan cheese.
Spray the back of a layer of tin foil and cover dish. Preheat oven to 350 degrees. Cook lasagna at 350 covered for 50 minutes. Remove foil and cook for 10 more minutes.