Preheat oven to 450°F (230°C). Position one rack in the center and another under the broiler.
Prepare the chicken marinade by whisking together olive oil, lemon zest, lemon juice, garlic, oregano, salt, and pepper in a bowl.
Add chicken thighs and toss until evenly coated. Marinate for 30 minutes at room temperature or up to 6 hours in the refrigerator.
Arrange sliced potatoes on a baking sheet. Drizzle with olive oil and half the lemon juice.
Season fries with oregano, smoked paprika, garlic powder, salt, and pepper. Toss well and spread into a single layer.
Roast fries for 20 minutes.
Remove fries, flip carefully, and return to the oven for another 10–15 minutes until golden and crisp.
Place marinated chicken on a separate baking sheet.
After flipping the fries, place the chicken in the oven and roast for 10–15 minutes until fully cooked.
Remove chicken and slice into bite-sized pieces.
For extra texture, place sliced chicken under the broiler for 4–5 minutes until lightly crisp and browned.
While everything cooks, prepare the yogurt drizzle by whisking together Greek yogurt, lemon zest, lemon juice, garlic, dill, salt, and pepper.
Add water as needed until the sauce reaches a drizzle-friendly consistency.
Finish the fries with the remaining lemon juice.
Assemble the Lemony Greek Chicken Pitas by filling warm pita bread with lettuce, fries, chicken, cucumber, feta, pickled onions, fresh dill, and a generous drizzle of herbed yogurt sauce.
Serve immediately and enjoy.