Heat 1 Tbsp olive oil in a large skillet over medium-high heat.
Season chicken with salt, pepper, Italian seasoning, garlic powder, onion powder, and lemon zest.
Add butter to the skillet, then cook chicken for 3 minutes per side until fully cooked. Remove and set aside.
Add remaining oil and butter to the same skillet.
Add zucchini and squash, season, and cook for about 4 minutes until tender.
Return chicken to the pan and drizzle with lemon juice. Toss everything together.
Sprinkle with parmesan and parsley. Serve warm with extra lemon zest if desired.