Preheat gas grill to medium-high. In a small bowl, whisk together olive oil, lemon juice, 1/2 tsp. salt and 1/2 tsp. garlic powder.
Combine lamb, allspice and remaining garlic powder and salt in a medium bowl and mix to incorporate. Form into 8 1/2-inch-thick patties. Grill patties, turning once, until an instant-read thermometer reads 160ºF, 5 to 7 minutes total.
Place chickpeas, greens, cherry tomatoes, cucumber, red onion, olives and feta, if desired, in a large bowl. Toss with dressing. Divide among 4 dinner plates. Top each portion with 2 lamb patties.
