Cook pasta according to package until al dente; reserve 1 cup pasta water, drain, and set aside.
Meanwhile, heat 2 tablespoons oil in large skillet over medium-high; cook zucchini, squash, and pepper 5-6 minutes until tender and lightly browned, stirring occasionally.
Cook garlic 1 minute until fragrant; add tomatoes and Italian seasoning. Cook 3-4 minutes until tomatoes start breaking down.
Stir in chicken; cook 2 minutes until heated through.
Add pasta and 1/2 cup reserved water; toss, adding more water if needed for light sauce.
Remove from heat; stir in remaining tablespoon oil, lemon juice, salt, and pepper. Top with Parmesan and basil; serve.