Make the batter: Preheat oven to 350 degrees F. Using a small brush, lightly coat two 9-inch cake pans with softened butter or vegetable-oil cooking spray. Dust with flour and tap out any excess. Set aside. In a medium bowl, sift together flour, baking powder, salt, and baking soda and set aside. In a large bowl using a mixer set at medium speed, cream butter and sugar until light and fluffy.
Add the eggs, one at a time, blending each thoroughly before adding the next. Scrape down sides and beat in vanilla extract. Reduce mixer speed to low and add the flour mixture by thirds, alternating with the lemon juice and buttermilk and ending with the dry ingredients.
Bake the cake: Divide the batter equally between the pans and spread evenly. Bake on the middle rack of the oven until the tops spring back when lightly touched and a tester inserted in the center of each cake layer comes out clean — 20 to 30 minutes.
Cool in the cake pans on a wire rack for 15 minutes. Using a knife, loosen the cake layers from the sides of the pans and invert the layers onto the wire rack to cool completely.
Frost the cake: Use a serrated knife to trim the cake layers to make them level, if necessary. Line the edges of a cake plate with 3-inch-wide strips of waxed or parchment paper and place a cake layer on top. Use a pastry bag or a plastic zip-top bag with a corner cut off to pipe a 1/2-inch-thick ring of Lemon Buttercream around the edge of the cake layer. Spread 1 1/2 cups Blackberry-Cassis Jam inside the buttercream ring and top with the second layer.
Place 1 cup of Lemon Buttercream on top of the cake and cover the entire cake with a thin coating of icing. Chill for at least 1 hour. Remove cake from refrigerator and frost with remaining icing.
Remove paper strips and serve at room temperature. Store refrigerated for up to 4 days.