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.