In a large mixing bowl, whisk together the olive oil, shawarma spice blend, and minced garlic to create the marinade.
Add the chicken pieces to the bowl, tossing well to ensure they are evenly coated. Cover and let marinate in the refrigerator for at least 30 minutes.
Cook the basmati rice according to package directions until fluffy. Set aside to cool slightly.
Preheat a grill or a large skillet over medium-high heat. Grill the marinated chicken pieces for 6-8 minutes per side, or until fully cooked through and slightly charred on the edges.
Remove the chicken from the heat and allow it to rest for 5 minutes before slicing.
In a small bowl, whisk together the Greek yogurt and lemon juice until smooth to create the yogurt sauce.
Assemble the bowls by layering the cooked basmati rice and chopped lettuce at the bottom. Arrange the grilled chicken, cherry tomatoes, cucumber, red onion, and bell peppers on top.
Drizzle the yogurt sauce over the assembled ingredients and serve immediately with wedges of warm pita bread.