For the dough, combine the water, yeast, sugar and olive oil in a large bowl. Let stand for 5 minutes until foamy. Stir both flours and salt into the yeast mixture until it forms a shaggy dough. Turn the dough onto a lightly floured work surface and knead for 10 minutes until the dough is smooth and elastic. (Alternatively, the dough can be mixed in the bowl of a stand mixer using a dough hook.)
Gather the dough into a ball, transfer to an oiled bowl and cover. Place the bowl in a warm spot to allow the dough to rise until it has doubled in size, about 2 hours.
Preheat a gas or charcoal grill on high heat.
On a lightly floured work surface, roll out the dough into a 12-inch diameter circle. Place the dough directly on the grates and grill for 3 minutes with the lid closed until the crust has grill marks and has puffed up. Turn over the crust and grill for an additional 2 minutes.
Spread the tomato sauce on the pizza leaving a 1-inch border at the edge. Scatter on the chopped sun dried tomatoes and sliced garlic. Sprinkle with cheese.
Continue grilling until the cheese has melted, about 2-3 minutes.
Toss the arugula with lemon juice, salt and pepper. Top the pizza with arugula before serving.