Remove dough from refrigerator; let stand at room temperature, covered, 30 minutes.
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).
Heat a large nonstick skillet over medium-high heat.
Add 4 teaspoons oil to pan; swirl to coat.
Add mushrooms and onion; saut 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.
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.