Heat 1 tablespoon olive oil in a large skillet over medium-high heat.
Pat the chicken dry with paper towels.
Season the chicken with salt, pepper, 2 teaspoons Italian seasoning, ½ teaspoon garlic powder, onion powder, and lemon zest.
Melt 1 tablespoon butter into the skillet with the oil.
Add the chicken and cook for about 3 minutes per side until fully cooked and the internal temperature reaches 165°F (74°C).
Transfer the chicken to a plate and loosely cover with foil.
Add the remaining olive oil and butter to the skillet.
Stir in the zucchini and yellow squash.
Season the vegetables with salt, the remaining Italian seasoning, and garlic powder.
Cook for about 4 minutes until just tender.
Return the chicken to the skillet.
Drizzle with fresh lemon juice and gently toss everything together.
Sprinkle generously with Parmesan cheese and chopped parsley.
Serve the Skillet Lemon Parmesan Chicken warm with extra Parmesan and lemon zest if desired. It pairs beautifully with cooked orzo, rice, mashed potatoes, or cauliflower rice.