Season the Chicken: Add the ground chicken, cumin, garlic powder, smoked paprika, cayenne pepper, salt, black pepper, olive oil, and lemon juice to a bowl and mix until evenly combined.
Assemble the Tacos: Divide the seasoned chicken evenly among the tortillas and press it into a thin, even layer over one side of each tortilla, spreading it close to the edges.
Cook the Tacos: Heat a large skillet over medium to medium-high heat and place the tortillas chicken-side down in the pan, working in batches as needed. Cook for 4–5 minutes, or until the chicken is browned and reaches an internal temperature of 165°F.
Crisp the Tortillas: Flip each taco and cook for another 1–2 minutes, or until the tortilla is lightly crisped, then transfer to a plate.
Make the Tzatziki: Combine the Greek yogurt, grated cucumber, lemon juice, olive oil, garlic, salt, and dill in a medium bowl and stir until well combined.
Finish and Serve: Top the chicken shawarma tacos with sliced cucumber, tomatoes, shredded lettuce, and a generous drizzle or spoonful of tzatziki, then serve immediately.