Heat grill on medium-high. Toss chicken with 1 tablespoon oil, then coriander, oregano and ¼ teaspoon each kosher salt and pepper. Thread onto skewers.
Place tomatoes and garlic on large piece heavy-duty foil. Sprinkle with 1 tablespoon oil and ¼ teaspoon each kosher salt and pepper. Fold and crimp foil to form pouch.
Place pouch and skewers on grill. Cook, shaking pouch and turning skewers occasionally, until chicken is cooked, 8 to 10 minutes. Just before removing from grill, brush chicken with 1 tablespoon lemon juice.
Meanwhile, in bowl, toss lettuce, onions and dill with remaining 2 tablespoons lemon juice, 1 tablespoon oil and ¼ teaspoon each kosher salt and pepper.
Serve chicken, tomatoes and salad with pitas and lemon.
