Preheat the oven to 350°F. Butter a 9-inch springform pan and coat with bread crumbs.
In the bowl of a stand mixer, or using a handheld mixer, beat the granulated sugar and eggs at high speed until creamy, 2 minutes. Beat in the melted butter and vanilla.
Zest the lemons to yield 1 tablespoon zest and beat into the batter. Juice the lemons to yield 1/3 cup juice and remove seeds.
Mix together flour and salt. At low speed, alternately beat in the flour and lemon juice until incorporated.
Pour the batter into the prepared pan and smooth the surface. Gently press in the nectarine slices and figs. Bake the cake on middle rack for 55-60 minutes, until a cake tester inserted in the center comes out clean with a few moist crumbs attached. You will notice the edges getting dark.
Transfer the cake to a rack to cool 10 minutes. Run a thin knife around the edge and remove from springform pan to cool completely. Dust the cake with powdered sugar to serve.