In a medium saucepan over medium heat add blueberries, sugar and lemon juice. Cook for 15 minutes until blueberries have cooked down into a sauce. Smash blueberries with a wooden spoon and stir often.
Run the blueberry reduction through a mesh strainer. Save the sauce and discard the pulp.
To a mixer or using a hand mixer blend butter and sugar until fluffy, about 2 minutes.
Add eggs and lemon juice and mix until well incorporated.
Mix in the flour and baking powder a little at a time on low. Mix until combined.
Add to a parchment lined 8x8 or 9x9 pan. Spread out.
Top with the blueberry sauce and swirl into the batter.
Bake at 350 for 25 minutes on the middle rack.
Cool for one hour.
Mix the icing together and pour over the cooled bars.
Cut into 16 squares with a sharp knife.
They taste better the longer they sit. I prefer them the next day. Store in an air tight container.