Place a pizza stone or baking sheet in oven. Preheat oven to 500°F. (Do not remove pizza stone while oven preheats.)
Heat oil in a large nonstick skillet over medium. Add shallot, and cook, stirring occasionally, until soft, 1 to 2 minutes. Add mushrooms and garlic; cook, stirring often, until liquid has almost evaporated, 5 to 6 minutes. Remove from heat. Sprinkle with 1/8 teaspoon salt, and set aside.
Roll dough into a 13-inch circle on a large piece of parchment paper; pierce well with a fork. Sprinkle goat cheese over dough; spread mushroom mixture over cheese. Top with mozzarella.
Toss arugula with lemon juice. Top pizza with arugula mixture; drizzle with truffle oil, if desired, and sprinkle with remaining 1/8 teaspoon salt. Cut into 8 slices.