Preheat oven to 375 degrees. Butter an 8-inch square baking pan; line bottom and two sides with a strip of parchment paper, leaving a 2-inch overhang. Butter paper; set pan aside.
In a food processor, pulse together 2 cups flour and 1 cup sugar. Add butter; pulse until mixture resembles coarse meal. Transfer half of mixture to prepared pan; with lightly floured fingers, press firmly into bottom. Set aside. Shape remaining mixture into large, moist clumps; transfer topping to a bowl, and set aside. Wipe food processor bowl clean.
Make filling: In food processor, blend figs, apple juice, lemon zest, and remaining 2 tablespoons each flour and sugar until a thick paste forms.
Using a small offset spatula or table knife, spread filling over crust. Sprinkle with topping. Bake until topping is golden brown, 60 to 65 minutes.
Transfer pan to a wire rack; let cool completely. Using paper overhang, lift crumble from pan, and transfer to a cutting board; cut into 20 bars.
Store cookies in an airtight container at room temperature, up to 5 days.