Let the prepared pizza dough sit for at least 30 minutes and up to 3 hours.
Preheat the oven to 500° and place a pizza stone in the bottom of the oven.
Mix the garlic with the lemon juice and mayonnaise in a small bowl. Season with salt to taste.
Heat one tablespoon olive oil in a medium frying pan. Add the onion, cover and cook over medium heat, stirring occasionally, until soft (approximately 8 minutes). Check seasoning.
To assemble, spread the pizza dough on a lightly floured work surface to a 12-inch round. Transfer the dough to a pizza pan and brush with olive oil. Sprinkle half the onion, tomatoes and Tonnino Tuna on the pizza and slide it onto the hot stone. Bake for 7 minutes until crusty and bubbling. Remove from the oven and sprinkle the pizza with half the aioli. Cover with half the basil and arugula.
Cut into pieces and serve.
To serve: Serves 3-4; can also be served in smaller pieces as an appetizer.