Preheat oven to 350 F.
Measure sugar into a small bowl. Zest both lemons over sugar, and rub zest and sugar together until the oils are well distributed. Sugar should feel like wet sand. Set aside.
In a separate bowl measure together cake flour, baking powder, baking soda and salt. Sift well and set aside.
Combine sugar and butter in a bowl and mix on medium high speed until well creamed - about 3 to 5 minutes.
With mixer on low speed slowly drizzle in oil into butter sugar mixture. Turn on medium speed and mix for 1 minute until well combined.
Add one egg to mixture and mix on medium low until well combined. Repeat with each egg making sure to mix well before adding the next.
Add lemon juice and mix on low until just combined.
Add ½ of dry ingredients to wet ingredients and mix on low until most of the flour is incorporated.
Add kefir and mix on low until just incorporated.
Add remaining dry ingredients to wet ingredients and mix on low until just a few streaks of flour remain.
Using a rubber spatula, gently fold in remaining flour until just combined.
Butter and flour 8x8 baking pan. Pour batter into baking pan and use spatula to distribute batter evenly.
Bake for 40 minutes or until toothpick comes out clean or with just a few crumbs.
Remove from oven and place on wire rack to cool. After 20 minutes remove cake from baking pan and allow to completely cool on wire rack.
Decorate with cream cheese frosting or American buttercream.