Grease and flour two loaf pans. Preheat oven to 350.
Zest 4 small lemons into a large bowl. Pulse granulated sugar in a food processor and add to the lemon zest. Mix together until no clumps remain. Set aside.
Peel and supreme the zested lemons. Place the lemon supremes in a small bowl. Set aside.
Cream together butter and lemon sugar. Add eggs in one at at time.
Sift together flour, powder, and salt. Add slowly into the wet mixture.
Mix in Greek yogurt.
Fold in lemon supremes.
Split batter evenly between loaf pans. Bake at 350 for 60-75 minutes, or until a toothpick inserted into the center of the cakes comes out clean.
Cool for 10 minutes and then remove from pans onto a cooling rack.
After the cakes have cooled, pour the icing over the cakes. Serve and enjoy!