1. Remove dough from refrigerator; let stand at room temperature, covered, 30 minutes.
2. Place a pizza stone or heavy baking sheet in oven. Preheat oven to 500° (keep pizza stone or baking sheet in oven as it preheats).
3. Heat a large nonstick skillet over medium-high heat. Add 4 teaspoons oil to pan; swirl to coat. Add mushrooms and onion; sauté 5 minutes or until slightly tender and mushrooms start to release liquid, stirring occasionally. Stir in garlic; cook 3 minutes or until lightly browned, stirring occasionally. Remove from heat.
4. Divide dough into 4 equal portions. Roll each portion into a 6-inch circle on a lightly floured surface; pierce entire surface of dough circles liberally with a fork. Carefully remove pizza stone from oven; sprinkle with cornmeal. Arrange dough circles on pizza stone. Combine cheeses in a small bowl. Divide cheese mixture into 4 equal portions; spread each portion evenly over 1 dough circle, leaving a 1/2-inch border. Divide mushroom mixture evenly among pizzas. Bake at 500° for 12 minutes or until crust is browned and crisp. Combine remaining 1 teaspoon oil, arugula, and lemon juice in a bowl. Divide arugula mixture evenly among pizzas. Cut each pizza into 4 wedges.