Preheat oven to 350 degrees. Lightly spray 2 9-inch round cake pans with cooking oil. Sprinkle with flour and tap out excess. In a medium bowl combine flour, baking soda, baking powder, and salt.
In a large bowl, cream butter and sugar until light and fluffy. Add eggs one at a time, mixing well between eggs. Stir in vanilla. Add about 1/3 of the flour mixture. Add lime juice and zest and mix well. Add half of the remaining flour mixture and buttermilk until incorporated. Add remaining flour mixture and mix well.
Pour batter into prepared pans and bake 20-30 minutes, until and inserted toothpick comes out clean and cake springs back when touched. Allow to cool on wire racks. Loosen edges with a knife and invert cakes on a flat clean surface.
For the frosting, whip cream and brown sugar until stiff peaks form. Stir in vanilla. Mash one cup of blackberries with a fork and mix into cream. Spread 1/3 of the frosting onto the top of one cake layer. Carefully place other cake on top. Use a rubber spatula to spread remaining frosting completely over the entire cake, coating top and sides well. Top with whole blackberries. Refrigerate until ready to serve.