Slice squashes in half length-wise, then cut into ½-inch thick pieces, pat dry and season with salt and pepper.
Bring water and salt for pasta to a boil in a large pot and cook pasta according to instructions, reserving ½ cup of the cooking water.
In a large, non-stick skillet, brown pine nuts over medium heat until fragrant and lightly browned (about 3 minutes). Set aside.
Add 1 tablespoon oil to the skillet and heat over high heat, add the zucchini and stir occasionally until browned on both sides (about 6-7 minutes). Transfer to a plate.
Add another tablespoon of oil, repeat with summer squash and set aside with zucchini.
Add another tablespoon of oil, heat and add onion, stirring for another 6-7 minutes or until translucent and lightly caramelized. Add garlic and lemon zest, stirring for under a minute, then add all squash and stir for about a minute or until hot and turn off heat.
When pasta is cooked, drain and add back into large pot along with ½ cup reserved pasta cooking water.
Add squash mixture, tomatoes, capers, pine nuts, olives, vinegar, lemon juice, parmesan cheese and remaining 3 tablespoons olive oil and toss.