Preheat grill. Brush grates with vegetable or corn oil.
In a small bowl, whisk together the 2T lemon juice and extra virgin olive oil. Place arugula leaves into a large bowl, and dress it with the lemon vinaigrette. Toss to mix well. Set aside. [I know it may seem like a lot of arugula at this point, but it will wilt down during the cooking process.].
Roll out pizza dough according to your recipe or store bought instructions. Once the grill is hot (you can hold your hands an inch over the grates for no more than 2 or 3seconds), carefully place the pizza dough onto the grill. Grill for about two minutes on one side. The pizza dough will also immediately puff up. Flip the pizza dough onto the other side and grill for another two minutes. Remove from grill onto a cookie sheet with tongs. Close the lid of the grill to retain its heat. [If you are using a ready-made pizza crust, cook it for two minutes on each side to get the grill marks and flavor.].
Place slices of smoked mozzarella around top of the pizza crust. And then in this order, spread all of the arugula leaves around, layer with prosciutto slices, and top with crumbled goat cheese.
Place the cookie sheet onto the grill and close the lid. [This allows for the toppings to cook without burning the pizza crust.] Cook for about five minutes, or until the cheese has melted, the arugula has wilted, and the prosciutto has crisped up a little. Carefully remove the cookie sheet from the grill. Using tongs, slide pizza onto a cutting board. Using a sharp knife or pizza slicer, slice the pizza and enjoy!