Preheat oven to 375°F. Grease and flour an 8-inch loaf pan.
In the bowl of an electric mixer fitted with the paddle attachment, cream butter and sugar at medium-high speed for about 3 minutes, until light and fluffy. With the mixer at low speed, add eggs, one at a time, lemon zest, and vanilla. Scrape the sides of the bowl as needed.
In a separate bowl, whisk together all the dry ingredients. Add flour mixture to butter mixture until just combined. Add sour cream and mix until all ingredients are combined but do not over beat.
Add batter into prepared loaf pan and bake for 55 minutes or until golden brown or when a toothpick inserted in the center comes out clean. Cool for 10 minutes in the pan and then transfer to a baking rack.
While cake is cooling, prepare lemon syrup. In a small saucepan, combine sugar and lemon juice and cook, stirring occasionally. Simmer for about 2 minutes until thickened slightly. Brush lemon syrup over pound cake. Cool at room temperature for at least 1 hour.
Prepare the glaze. Combine powdered sugar and the lemon juice in a small bowl, mix until smooth. Pour over the pound cake.