In a large bowl, combine the olive oil, cumin, coriander, smoked paprika, turmeric, garlic powder, onion powder, salt, black pepper, cayenne pepper, and lemon juice. Mix well to create a marinade.
Add the chicken thighs to the marinade, ensuring they are well coated. Cover and refrigerate for at least 1 hour, or up to overnight for best flavor.
Preheat your grill or a grill pan over medium-high heat.
Remove the chicken from the marinade and grill for about 6-7 minutes per side, or until the chicken is cooked through and has nice grill marks.
Once cooked, let the chicken rest for 5 minutes before slicing it into thin strips.
To assemble the tower, place a pita bread on a plate, layer with sliced chicken, Greek yogurt, cucumbers, tomatoes, red onion, and parsley. Drizzle with tahini if desired.
Repeat with the remaining pita breads and ingredients to create additional servings.