Preheat the oven to 350°F (175°C). Grease and flour an 8-inch round cake pan.
In a large bowl, sift together the all-purpose flour, baking soda, baking powder, and salt.
Add the granulated sugar to the dry ingredients and mix well.
In a separate bowl, whisk together the plain yogurt, vegetable oil, fresh lemon juice, lemon zest, water, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and gently fold together using a spatula until just combined. Do not overmix.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake in the preheated oven for 30 to 35 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes.
Turn the cake out onto a wire rack and let it cool completely before serving.