Slice potatoes very thin with a mandoline, and place in a bowl. Pour lemon juice over potatoes, and add a pinch of coarse salt. Let sit at least 1 hour 30 minutes.
Heat a large skillet over medium heat, and add 1 tablespoon oil. Add onions, and stir to coat. Reduce heat to low, and cook 10 minutes. Season onions with coarse salt, and cook, stirring frequently, until rich brown in color, 45 minutes to 1 hour (add a little water to skillet if onions begin to stick). Remove from heat, and let cool.
Heat remaining oil and the rosemary in a small saucepan over low heat 15 minutes (do not let boil). Let cool, then pour through a fine sieve into a bowl.
Meanwhile, place a pizza stone on middle rack of oven, and preheat oven to 500 degrees, at least 30 minutes. Divide dough into 2 pieces, and form each into a ball. Loosely cover with a kitchen towel or plastic wrap, and let stand 15 minutes. Roll each ball of dough into a 12-inch round or an oval about 1/8-inch thick on a lightly floured work surface with a lightly floured rolling pin (or stretch it with your hands). Lightly dust a wooden pizza peel with cornmeal, and place 1 round of dough on peel. Generously brush dough with rosemary oil. Place half the onions on dough, leaving a 1/2-inch border. Drain potatoes, discarding lemon juice, and cover onions with half the potatoes. Crumble half the goat cheese over potatoes.
Slide pizza from peel to pizza stone, and bake until crust is golden brown and potatoes are cooked, 10 to 12 minutes. Transfer pizza to a cutting board, and sprinkle with sea salt. Repeat with second pizza.