Preheat the oven to 350 degrees F. Spread the pitas on a baking sheet and bake until crisp and golden, about 10 minutes. Set aside.
Meanwhile, preheat a grill to medium high. Combine the ground beef, grated red onion, 1 tablespoon each olive oil and harissa, and 1/4 teaspoon each salt and pepper in a large bowl. Mix with your hands until just combined. Form into four 1-inch-thick patties; set aside.
Whisk the lemon juice with the remaining 1 tablespoon harissa in another large bowl. Gradually whisk in the remaining 2 tablespoons olive oil. Add the tomatoes, cucumbers, herbs and sliced red onion; toss to coat. Set aside.
Brush the grill grates with oil. Grill the burgers about 4 minutes per side for medium rare. Add the lettuce and pita wedges to the salad bowl; toss. Top each serving of salad with the feta and burgers.