Preheat an oven to 170°C. Prepare one pound cake tin (regular size) or 2 smaller pound cake tins. Butter up the tin and attach the attachment paper to it.
Start with creaming butter and sugar. Whisk the butter and sugar with an electric mixer on high speed for 3 minutes. You should end up with creamy and soft consistency in the mixture.
Continue by adding eggs, one at a time. Whisk on medium speed and scrape the sides of the bowl when needed. Mix until the batter is runny and creamy.
In one bowl mix flour with baking powder and lemon zest - whisk with an egg whisker. Into another bowl add yogurt with lemon zest, lemon juice, and vanilla extract.
The next step is crucial - start by adding 1/3 flour mixture into the batter, while mixing on low speed. Then add 1/2 yogurt liquid. When it's well combined, add flour mixture, mix, yogurt mixture. In the end, add the rest of the flour mixture. Don't forget the scrape down the sides of the bowl while the batter is mixing.
Now, I recommend tasting the batter if it's lemony enough. If not, you can add more lemon zest or lemon juice. However, in this case, don't forget to add a little bit of flour and combine it with a spatula (2 tbsps of flour).
Pour the batter into the pound cake tin and bake for 50 minutes or until the wooden toothpick comes out clean.
Take cake out of the oven and let cool in the tin for 10 minutes. Then take it out and allow to cool for the next 30 minutes.
For lemon icing - prepare icing sugar into the bowl. Pour the lemon juice and mix with an egg mixer until it's well combined. The icing should be thick enough to stay on the cake. I like doing 2 layers. The first one is a little runny and I cover the cake with it while the cake is still warm (not hot). Then I let the cake cool. You can stop at this point. But for nicer white cover and more lemon taste, repeat the process but add more icing sugar. The batter should be as thick as the pancake batter. If not, add more icing sugar. You can also add lemon zest. Cover the cake with a thick layer. On top of the cake, you can sprinkle extra lemon zest and a few drops of lemon juice. Trust me, you will not regret doing it.