Preheat the oven to the hottest temperature that the oven will go, preferably 500ºF. Place the brick on the bottom shelf of the oven to preheat. Grate the two cheeses and combine.
Combine 2 tablespoons olive oil and garlic and let sit 30 minutes.
Heat 2 tablespoons olive oil in a large skillet and saute onions until soft, 10 minutes. Add the lamb, tomatoes, tomato paste, parsley, pine nuts, spices, 1/4 teaspoon salt and 1/4 teaspoon black pepper and cook slowly, uncovered 10 minutes. Add lemon juice and mix well.
Roll the pizza into the desired shape. It should be 1/4-inch thick. Transfer it to a heavily floured pizza peel. Brush the dough to within 1/2-inch of the edge with the garlic oil. Sprinkle half of the combined cheese on top and then half of the spiced lamb mixture. Transfer the pizza onto a stone and bake it in the hottest temperature that your oven will go. Cook until golden and crisp, 8 to 10 minutes.