Arrange 1 1/2 cups lettuce and 2 tablespoons onion in each of 4 (4-cup) bowls or containers. Top each serving with 1/3 cup chickpeas, 1/2 cup tomatoes, 1/2 cup cucumber, 4 olives, and 2 cheese slices.
Whisk together oil, vinegar, lemon juice, oregano, pepper, salt, and garlic in a small bowl. Serve about 2 tablespoons dressing with each salad.