Prepare a grill for medium-high heat. Line a baking sheet with parchment paper.
Finely grate the zest of the lemon; cut the lemon in half and reserve. Stir together the ricotta, lemon zest, 1/4 teaspoon salt and a few grinds of black pepper. Set aside.
Divide the pizza dough into 2 balls. Sprinkle the flour on a clean flat surface and roll each ball into an oval about 14 inches long, 6 or 7 inches across and between 1/8 and 1/4 inch thick. Transfer the crusts to the prepared baking sheet. Brush both sides of each crust with olive oil, about 1 tablespoon per side, and lightly sprinkle with salt.
Lightly oil the grill grates. Grill the crusts until they start to puff and distinct grill marks appear, about 1 minute. Flip and cook until just cooked through, an additional 1 to 2 minutes. Discard the used parchment paper and put the finished crusts on the baking sheet.
Immediately top each crust evenly with prosciutto. Place small dollops of the ricotta mixture over the prosciutto. Toss the arugula in a bowl with the remaining 1 tablespoon olive oil and the juice of one of the lemon halves (reserve the other half for another use). Season with salt and pepper. Divide the arugula between the pizzas and serve.
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