Preheat oven to 375 degrees. Grease a 9 x 5 inch loaf pan.
Beat together the butter, sugar, and lemon zest until creamy, about 2-3 minutes. Whip in the eggs, one at a time, then beat in the Greek yogurt, lemon juice, and vanilla. Add the flour, baking powder, baking soda, and salt. Beat until just combined.
Scoop the batter into the loaf pan. Bake 35-40 minutes until the center is no longer jiggly and an inserted toothpick emerges with just a few moist crumbs. Cool 5 minutes in the pan, then invert onto a wire rack. Cool completely.