1. Cake: Preheat oven to 350 degrees. Lightly coat three 8-by-2-inch round cake pans with cooking spray. Line bottoms with parchment. In a large bowl, whisk together flour, cocoa, baking soda, and salt. In another large bowl, beat butter with sugar on high speed until light and fluffy, 3 minutes. Add eggs, one at a time, beating well after each addition. Beat in liqueur. Reduce speed to low and add flour mixture in three batches, alternating with buttermilk in two batches. Beat to combine, scraping down sides of bowl as needed. Beat in melted chocolate.
2. Divide batter evenly among prepared pans, smoothing tops with an offset spatula. Bake, rotating pans halfway through front to back and top to bottom, until a tester inserted in centers comes out clean, about 25 minutes. Let cakes cool in pans on a wire rack 10 minutes. Run a small sharp knife around edges, then invert onto rack. Remove parchment and let cool completely, about 25 minutes. With a serrated knife, trim tops of cakes so they’re level.
3. Filling: While cakes are baking, stir together 3 cups raspberries, sugar, salt, and lemon juice in a medium saucepan. Cook over high, stirring frequently and mashing with the back of a spoon, until mixture comes to a boil, 2 minutes. Continue to cook, stirring, until mixture thickens and clings to spoon, 7 to 8 minutes more. (You should have 1 1/3 cups.) Let cool 30 minutes. Stir in 2 cups raspberries, reserving remainder.
4. Spread half of filling over one cake. Top with second layer; spread remaining filling over top. Top with final layer, cut-side down. Refrigerate, covered, at least 1 hour and up to overnight. Spread frosting over top and sides of cake. Garnish with remaining raspberries.