Heat grill to medium-high. Sprinkle 1⁄4 teaspoon salt over the garlic; using a large knife, rub and scrape salt into the garlic to make a paste. Transfer to a large bowl.
Finely grate lemon zest into the bowl, then squeeze in juice (you should have 3 tablespoons). Whisk in mustard, Worcestershire, anchovy, and 2 tablespoons oil. Stir in 1/4 cup Parmesan.
On a lightly floured surface, shape pizza dough into a 12" oval or rectangle. Place on a baking sheet.
Rub chicken with 1 teaspoon oil and season with 1⁄4 teaspoon each salt and pepper. Grill until cooked through, 4 to 6 minutes per side. Transfer to a cutting board.
Brush the top of the pizza dough with remaining 1 teaspoon oil. Transfer to the grill, oiled-side down, and cook, covered, until the top begins to bubble and the bottom becomes crisp, about 2 minutes. Turn over, sprinkle grilled side with 1⁄4 cup Parmesan and cook, covered, until the bottom is golden brown and crisp, 2 to 3 minutes. Transfer to a cutting board.
Slice the chicken. Toss the lettuce with dressing, then gently fold in chicken. Spoon salad on top of the flatbread. Serve with pepper and additional Parmesan, if desired.
Ingredients