Preheat the oven to 350°F (176°C). Grease and flour a Charlotte Cake Pan (6 cups capacity) if using or grease and line a 8-inch round cake pan.
Whisk flour, baking powder, baking soda and salt into a bowl. Set aside.
Mix yogurt and lemon juice together, set aside.
In a mixing bowl, add in butter, sugar and lemon zest. With the paddle attachment, start beating on medium high for about 2-3 minutes (scrape the bowl with a spatula half way through) until light and fluffy.
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.
Add half the dry ingredients and mix on low for a few seconds then add in yogurt and lemon juice, mix. Finally add the rest of the dry ingredients and mix until just combined.
Transfer the batter to the prepared pan and bake in the preheated oven for about 25-30 minutes or until a toothpick inserted in the center comes out clean. In the meantime, prepare the syrup.
Combine lemon juice and sugar in a sauce pan and bring to a boil on medium high heat. Reduce the heat to low and simmer for 5 minutes until slightly thickened. Add the lemon peel and take the pan off the heat. Let it cool down for 15 minutes.
When the cake is baked, let it cool down in the pan for 10 minutes, then invert it on a serving plate.
Using a toothpick, poke many holes on the surface of the cake. Using a spoon, slowly pour the syrup on top. Let it soak and for the cake to cool down completely before frosting.