Over medium-high heat, cook sausages in a pan until no longer pink in the center. Remove from heat and let sit for around 5 minutes. The slice in half lengthwise.
In a bowl, add sliced onion and summer squash. Sprinkle with olive oil, salt, pepper and oregano. Toss to coat.
In a deep 13x9 baking dish, add a small amount of sauce to cover the bottom. Then add a layer of lasagna sheets. Top with half of squash mixture then one cup of mozzarella cheese and ⅓ cup of parmesan cheese. Next add half of split sausages and pour ⅓ of tomato sauce.
Repeat entire set of layers. Then top with another layer of lasagna sheets, remaining sauce and remaining cheese. Top with fresh basil, if desired. Cover with foil and bake in oven for 45 minutes.
Remove from oven and remove foil. Return to oven to bake another 15 minutes.
Let rest at least 10 minutes (20 minutes are better) before cutting and serving.