Preheat a grill to medium-high. Using a food processor, puree the parmesan, 1/4 cup olive oil, garlic, lemon juice and anchovy.
Cut the pizza dough into 4 pieces. On a baking sheet, rub the dough with the remaining 1 tablespoon olive oil and press each piece into a 4-by-8-inch rectangle. Place the dough on the grill, cover and cook until browned on one side, 3 to 4 minutes. Turn and grill until cooked through, about 3 minutes.
Brush one side of each pizza with the anchovy dressing. Top with the lettuce and tomato; drizzle with the remaining dressing.