Preheat oven to 450°. Roll out dough on a floured surface to a very thin 10-inch round. Place dough onto a baking sheet, prick all over with a fork, and bake for about 10–15 minutes.

Meanwhile, heat 2 tablespoons olive oil and balsamic vinegar in a small saucepan over medium heat. Add red onion and figs; increase heat, sautéing until figs are thoroughly coated.

Remove pizza crust and brush with olive oil. Spread preserves onto crust and then scatter with thyme, goat cheese, and fig-onion mixture. Return to oven and bake for another 5–10 minutes or until crust is browned to your liking.

Toss arugula with remaining 1 teaspoon oil and lemon juice in a large bowl; season with salt and pepper. Top finished pizza with arugula mixture and serve.