Preheat the oven to 350 degrees F. Cream the butter and sugar in a medium bowl using a hand mixer until light and fluffy, about 3 minutes. While still mixing, slowly add the eggs, then the vanilla. Whisk together the flour, baking powder and salt in a small bowl. Add half the flour mixture to the butter mixture and mix. Then add the lemon juice and zest. Mix, then add the remaining half cup of the flour mixture. Pour into a greased 8-inch square pan. Bake until the cake springs back when lightly pressed, about 20 minutes.