Preheat oven to 350F. Prepare two 8 inch pans by spraying with non-stick spray. Line the bottom with a parchment paper circle and flour the sides of each pan.
In a medium bowl, sift together the self-raising flour, baking powder and salt. Set aside.
In the bowl of a stand mixer or in a large bowl with a hand mixer, beat together the butter and sugar on medium speed for 3 minutes.
In a small bowl, whisk the eggs briefly. Slowly add a little bit of the eggs at a time. Mix after each addition. Add the vanilla and lemon zest and mix until incorporated.
Gradually add the flour mixture with the mixer on low speed. Once all of the flour has been added, mix for an additional 20 seconds.
Divide the batter evenly between the two pans. Spread the batter into an even layer in each pan. Bake for 30 to 35 minutes or until a toothpick comes out clean when poked in the center of the cake.