Line the bottoms of two 9-inch diameter cake pans with parchment paper. Spray paper and sides with cooking spray.
Preheat oven to 350 F.
Sift flour, baking soda, and salt and set aside.
Cream butter and sugar together until light and fluffy with a mixer or hand-held beater. Add the beaten eggs and beat well, until very fluffy. Stir in vanilla.
Stir flour mixture into batter alternately with milk, beginning and ending with dry ingredients. Then stir in lime juice.
Divide batter equally between the two prepared pans.
Bake for 25-30 minutes, or until a cake tester inserted into the middle of the cake comes out clean.
Cool cakes completely on cake racks and remove the paper from the bottom.