Preheat oven to 350 F / 180 C & place rack in middle position. Butter and line with parchment paper loaf pan 9 × 5 inch.
In a medium bowl, cream the butter with sugar with electric mixer & add one egg at a time. Mix well to combine.
In another medium bowl, add all-purposed flour with baking powder, baking soda, salt and zest of lemon. Stir and set this aside
Use measuring cup to mix this following ingredients. Measure lemon juice, add milk and vanilla extract. Stir it all well, to combine. Add this lemon mixture into the butter batter by alternating with the flour mixture.
Start first with one third of the dry mixture & mix to combine. Then add one third of the liquid mixture & mix to combine. Continue adding alternatively, until you use all the dry & liquid mixtures. Make sure you combine well all the ingredients. At the end, use spatula to scrape the bowl from sides.
Pour the batter in prepared loaf pan and bake on 350 F / 180 C for 45 minutes. Once baked, remove from oven and place on cooling rack for 10 minutes.