In a medium-size skillet over medium-high heat, heat the oil and cook the onions and the garlic until softened, about 5 minutes. Add the chicken and cook until browned, about 6 minutes. Add the next 5 ingredients (tomatoes through oregano) and season with sea salt and pepper to taste. Turn heat down to low and let simmer for about 10 minutes.
To prepare the lasagna, in a medium-large size baking dish, alternating layers of summer squash slices with layers of the meat sauce. Keep making layers until all of the ingredients have been used.
Bake for 25 minutes or until the squash is soft and tender. Serve warm garnished with parsley.