Preheat oven to 350°F degrees. Line a 9×5 loaf pan with parchment paper.
In a large mixing bowl, cream together the sugar and butter. Add in eggs and Greek yogurt and mix until smooth. Finally, add in lemon juice, lemon zest, vanilla extract, and mix.
Mix in ~1/2 cup flour along with the baking powder, baking soda and salt. Then, mix in the remaining flour ½ cup at a time. Do not overmix.
Pour batter into prepared loaf pan. Bake for about 45-52 minutes, or until a toothpick comes out clean.
Allow loaf to cool for at least 30 minutes. Remove loaf from pan and allow to cool completely in the parchment paper before glazing.
For the glaze: in a medium bowl, combine the powdered sugar, lemon juice and melted butter until smooth and combined.
Evenly spread or drizzle glaze over loaf before slicing and serving.