Preheat oven to 350 degrees F. Grease and flour a loaf pan.
Combine eggs and sugar.
Add lemon zest, lemon juice and lemon extract.
Add vegetable oil and mix.
Gradually add greek yogurt and mix until combined.
Stir in baking powder.
Slowly add flour. Blend until smooth.
Pour the batter into the baking pan. Bake for 45 minutes. Remove from the oven and quickly cover the pan with aluminum foil, and return to the oven, for the last 10 minutes, to prevent excess browning.
Cool the loaf in a pan for 15 minutes. Remove from pan to wire racks to cool completely.
Whisk confectioners' sugar with lemon juice until smooth. Spoon evenly over the loaf and let sit for about 30 minutes.