Heat grill to high (450° to 550°). Mix 1 tbsp. each lemon juice and oil, 1 tsp. garlic, and 1/2 tsp. each salt, pepper, and cumin in a medium bowl. Add chicken and turn to coat.
Grill chicken, turning once, until cooked through and browned, about 10 minutes. Let rest, covered, 5 minutes.
Whisk together remaining 2 tbsp. each lemon juice and oil, 2 tsp. garlic, 1/2 tsp. each salt and pepper, and 1 tsp. cumin with the tahini in a large bowl. Add chickpeas, tomatoes, onion, and bell pepper and toss to coat. Divide among 4 plates. Slice chicken and set on top. Sprinkle salads with parsley and cheese.
Note: Nutritional analysis is per serving.