Preheat the oven to 350 degrees. Spray three six inch round cake pans with baking spray. Line with parchment rounds and spray again.
In a bowl, sift together the flour, salt, and baking powder. Set aside.
In the bowl of an electric mixer, using the paddle attachment, beat the butter on medium speed for two minutes, until it is creamy. Then, add the sugar and beat four minutes until fluffy. Then, add the beaten eggs, one at a time, and blend until just combined. Then, add the lemon extract and stir until just combined. Scrape down the sides of the bowl as needed. Then, add the flour and milk in 5 parts, starting and ending with the flour, and beat on low until just combined.
Bake the cakes for 17 minutes, or until a toothpick inserted in the center of the cake comes out clean. Let the pans cool on a rack for ten minutes, and then remove them from the pans. Let them cool completely on the racks.
For the Cream Cheese Frosting: In a mixing bowl, beat together the cream cheese, vanilla, and butter. Then, sift in the powdered sugar, and whip until blended.
Spread frosting all over the cake, between the layer, on the sides, and on top.