Heat 1 tablespoon olive oil in a large non-stick skillet over medium-high heat.
Pat the chicken dry with paper towels. Season with salt, black pepper, 2 teaspoons Italian seasoning, 1/2 teaspoon garlic powder, onion powder, and lemon zest.
Melt 1 tablespoon butter into the skillet with the olive oil.
Add the seasoned chicken and cook for about 3 minutes per side until golden and fully cooked. The internal temperature should reach 165°F.
Transfer the chicken to a plate and loosely cover with foil.
Add the remaining olive oil and butter to the same skillet.
Add zucchini and yellow squash. Season with salt, remaining Italian seasoning, and remaining garlic powder.
Cook the vegetables for about 4 minutes, stirring occasionally until tender-crisp.
Return the chicken to the skillet.
Drizzle fresh lemon juice over the Skillet Lemon Parmesan Chicken with Zucchini and Squash and toss gently.
Sprinkle with parmesan cheese and fresh parsley.
Serve warm with extra lemon zest and parmesan if desired.