Toast the pita bread in a toaster oven until crisp but not browned.
Heat 3 tbsp of olive oil in a large pan. Break the pita bread into pieces, and fry briefly until browned. Add salt, pepper, and 0.5 tsp sumac. Remove the pita chips from the heat and drain on paper towels.
In a large bowl, combine chopped lettuce, cucumber, tomatoes, green onions, sliced radish, and parsley.
To make the lime vinaigrette, whisk together lime juice, olive oil, and spices in a small bowl.
Dress the salad with the vinaigrette, add the pita chips, more sumac if desired, and toss lightly. Transfer to serving bowls or plates. Enjoy!