Bring broth and water to boil in large saucepan over high heat. Reduce heat to medium-low to maintain gentle simmer.
Heat 2 tablespoons butter in large Dutch oven over medium heat. When butter has melted, add onion and ¾ teaspoon salt; cook, stirring frequently, until onion is softened but not browned, 4 to 7 minutes. Add garlic and stir until fragrant, about 30 seconds. Add rice and cook, stirring frequently, until grains are translucent around edges, about 3 minutes.
Add wine and cook, stirring constantly, until fully absorbed, 2 to 3 minutes. Stir 5 cups hot broth mixture into rice; reduce heat to medium-low, cover, and simmer until almost all liquid has been absorbed and rice is just al dente, 16 to 19 minutes, stirring twice during cooking.
Add ¾ cup hot broth mixture and stir gently and constantly until risotto becomes creamy, about 3 minutes. Stir in diced figs and Parmesan. Remove pot from heat, cover, and let stand 5 minutes. Stir in remaining 2 tablespoons butter, lemon juice, parsley, and chives; season with salt and pepper to taste. If desired, add up to 3/4 cup remaining broth mixture to loosen texture of risotto. Serve immediately.