Preheat the oven to 450°F (230°C). Position one rack in the center and another directly beneath the broiler.
In a medium bowl, whisk together olive oil, lemon zest, lemon juice, garlic, oregano, 1½ teaspoons kosher salt, and black pepper. Add the chicken thighs and toss until fully coated. Marinate for 30 minutes at room temperature or refrigerate for up to 6 hours.
Line a large baking sheet with foil if desired. Arrange the sliced potatoes on the baking sheet.
Drizzle the potatoes with olive oil and half of the lemon juice. Sprinkle with oregano, smoked paprika, garlic powder, salt, and pepper. Toss well and spread into an even layer.
Roast the fries on the center oven rack for 20 minutes.
Remove the fries from the oven and carefully flip them with a spatula. Return them to the oven for another 10–15 minutes until golden and crisp.
Squeeze the remaining lemon juice over the fries immediately after roasting.
Place the marinated chicken on a separate baking sheet.
When the fries are flipped, place the chicken in the oven on the upper rack. Roast for 10–15 minutes or until fully cooked.
For extra texture, slice the cooked chicken into bite-sized pieces and return it to the baking sheet. Broil for 4–5 minutes, turning the pan halfway through, until lightly browned and crisp.
While everything cooks, prepare the yogurt drizzle. In a small bowl, whisk together Greek yogurt, lemon zest, lemon juice, garlic, dill, salt, and pepper.
Add water as needed until the desired consistency is reached.
Warm the pita bread for 1–2 minutes in the oven.
Assemble the Lemony Greek Chicken Pitas by filling warm pita bread with lettuce, roasted fries, chicken, cucumber, pickled onions, feta, and fresh dill.
Finish with a generous drizzle of herbed yogurt sauce and serve immediately.