In a small bowl, stir together the yeast, 1 tablespoon flour, 1/4 cup warm water, and pinch of sugar. Mix and let stand about 5 to 10 minutes until mixture has started to foam.
In a large bowl, stir together 1 1/4 cups flour with salt. Add yeast mixture, olive oil, and remaining 1/2 cup warm water; stir until smooth. Add enough flour (about 1/2 cup) to make dough come away from the sides of the bowl. The dough will still be rather wet at this point.
Remove dough from bowl. Divide in two if making two pizzas. Shape into balls and place on a board or counter. Cover with a damp cloth and allow to rise until doubled in size, about 90 minutes.
Heat a pizza stone on the bottom rack of the oven for an hour at 500°F, or heat an unrimmed cooking sheet in a preheated oven for five minutes.
Pat dough ball into a thin circle. If making one large pizza, sprinkle half the mozzarella over the dough, spread prosciutto over mozzarella, then layer lemon slices on top without covering the prosciutto completely. Next, add the rest of the mozzarella over the lemon, followed by all the Parmigiano. If making two smaller pizzas, divide the toppings accordingly.
Place the pizza on the pizza stone or cooking sheet in the oven. Bake until crust is golden and slightly darkened around the edges, and cheese is bubbling, about 10 to 12 minutes. Remove the pizza from the oven.
Scatter arugula over the top of the pizza, then drizzle with a little extra-virgin olive oil. Cut into slices and serve.