Preheat the oven to 350°F (175°C). Grease and flour an 8-inch baking pan.
In a bowl, mix flour, baking powder, baking soda, and salt. Set aside.
Beat butter and sugar until light and fluffy. Add eggs, one at a time, then mix in lemon zest, juice, and vanilla.
Gradually mix in dry ingredients and sour cream. Stir until just combined.
Pour the batter into the prepared pan and smooth the top.
Bake for 30 minutes or until a toothpick inserted comes out clean.
Cool the cake in the pan for 10 minutes, then transfer to a wire rack.
For the glaze, whisk powdered sugar, lemon juice, and zest. Drizzle over the cooled cake.