Preheat oven to 350°F (180°C). Grease and flour a 9-inch cake pan, or line with parchment paper.
In a large bowl, sift together flour, baking powder, baking soda, and salt.
Zest and juice the lemons, set aside.
In a large bowl, beat eggs and sugar until pale and fluffy (about 3-4 minutes).
Gradually incorporate the oil while continuing to beat.
Add kefir, lemon zest, lemon juice, and vanilla extract. Mix well.
Gently fold in the dry ingredients in several additions, mixing until just combined to form a smooth batter.
Pour the batter into the prepared pan.
Bake for 45 minutes, or until a toothpick inserted in the center comes out clean.
Let cool in the pan for 10 minutes before turning out onto a cooling rack.