For this cake, it is crucial that the eggs and butter are at room temperature. So make sure you take them out of the fridge 1 hour before you start.
Preheat the oven to 325°F (163°C). Grease and line a 9x5 loaf pan with parchment paper, leaving some overhang by the sides. Sift flour, baking powder and salt into a small bowl. Set aside.
Add lemon juice to the buttermilk, mix and set aside.
In a large mixing bowl, add in butter and sugar. With the paddle attachment, start beating on medium for about 2-3 minutes (scrape the bowl with a spatula half way through) until light and fluffy.
Add the lemon zest and mix until combined.
Add the eggs one at a time, mixing well after each addition (about 30 seconds). Scrape the sides of bowl to make sure everything is combined. Add vanilla extract and mix.
Mix in the dry ingredients in 3 parts, alternating with buttermilk and lemon juice mixture, beating well after each addition. This means, adding one third of the dry ingredients, mixing a little bit until incorporated, then adding half of the buttermilk lemon juice mixture and mixing until combined. Then, add another one third of the dry ingredients, mix, add the rest of the buttermilk, mix, and finally add the last part of the dry ingredients. So, we start and finish with the dry ingredients.
Transfer the batter to the prepared pan and bake in the preheated oven for about 55-60 minutes or until a toothpick inserted in the center comes out clean. In the meantime, we prepare the lemon syrup.