To marinade the chicken, in a large bowl, combine the chicken, yogurt, red onion, garlic, lemon juice, olive oil, herbs and spices to fully incorporate. Cover with plastic wrap and place in the fridge for at least 1 hour or overnight.
Preheat oven to 375°F and line a baking sheet with foil. Place the chicken on the baking sheet, in an even layer and bake in the oven for about 20 minutes or until crispy and cooked through. Remove from oven and allow to cool down. Then cut into small pieces with a large knife or shred with your fingers.
Heat a large skillet over pot over medium heat with about 3-inches of vegetable oil. Cut the lavash in half so you end up with 8 rectangles. Fill one end with chicken and roll into a tight log, securing the edges with a few toothpicks to keep it formed. Once the oil is hot, carefully drop in the taquitos, a few at a time, and fry for about 1 to 2 minutes on the first side. Flip over and fry for another minute or until golden brown and crispy. Place on a plate or platter lined with paper towels and then transfer the taquitos to a wire rack set over a baking sheet. Continue frying until all the taquitos are done. Rewarm in the oven.
To make the sauce, combine all of the ingredients in a food processor or blender and blend until creamy and smooth.
Right before serving, top the taquitos with lettuce, tomatoes, cucumber, feta, onion, olives and the sauce. Enjoy!