Preheat oven to 350 degrees F. Grease 9 x 5 inch loaf pan.
Stir flour, baking powder and salt together in a medium bowl. Set aside.
Zest the 2 lemons and place lemon zest in a bowl. Put the lemons to the side. Add sucanat, Greek yogurt, butter in with the zest with an electric mixer until fluffy, about 2-3 minutes. Beat in one egg white at a time, then add whole egg. Continue to beat. Reduce speed to medium and beat in the milk and lemon juice.
Reduce the mixer to low and add in the flour mixture, only beating until combined. Do not overmix.
Bake the cake until toothpick comes out clean when placed in the center, about 50 minutes. Let the cake cool for 15 minutes. Run a knife around the sides of cake and let cool on wire rack.
While cooling, place sucanat and lemon juice for the glaze in a small saucepan and place on the stove. Cook for 1-2 minutes until it becomes thick while stirring constantly. *Note: The glaze will NOT be white because sucanat is not white. The glaze is a brownish color that you really can not see when placed on the cake.
Poke small holes in the top of the cake. Place a baking tray underneath the wire rack to avoid a mess. Pour glaze on top of cake making sure it gets into all of the poked holes. Let the cake cool completely before slicing.