Put an inverted baking sheet on the lowest oven rack and preheat to 400 degrees F. Divide the pizza dough in half. Press and stretch 1 piece into an 8-by-10-inch rectangle on an oiled surface using oiled hands; brush with 2 teaspoons olive oil.
Layer 1 cup spinach, half each of the artichokes, salami and provolone and 1/2 tablespoon parmesan on the dough, leaving a 1-inch border on the short sides and a 2-inch border on the long sides. Fold in the short sides, then the long sides, stretching to cover the filling; pinch at the seam. Repeat to make a second stromboli.
Arrange the stromboli seam-side down, 2 to 3 inches apart, on a piece of parchment; slide onto another inverted baking sheet. Cut a few slits into the tops and brush each with 2 teaspoons olive oil; sprinkle with the remaining 1 tablespoon parmesan. Slide the stromboli (on the parchment) onto the hot baking sheet. Bake until the crust is golden brown, about 25 minutes. Cool slightly.
Toast the walnuts in a dry skillet over medium heat, 5 minutes; cool. Toss the celery, the remaining 4 cups spinach and 2 tablespoons olive oil, the lemon juice and walnuts in a large bowl; season with salt and pepper. Cut each stromboli in half and serve with the salad.