Line a 9-inch square baking pan with parchment paper or spray with cooking spray.
Beat together the butter and sugar until fluffy. Add the egg.
Once egg is incorporated, add lemon juice and combine.
Whisk together flour, baking powder and salt, then add to the wet ingredients, mixing until just combined.
Fold in the blackberries.
Using a rubber spatula, spread the batter into the prepared pan.
Bake 30-35 minutes, until cooked through. Edges will be slightly browned and a toothpick inserted in the center will come out clean. Let cool completely (about 1 hour).
In a small saucepan combine blackberries, sugar and lemon juice. Bring to a boil, reduce heat and simmer 2-3 minutes, until sugar dissolves and the blackberries start to break down. Process with a food processor or blender, then pass through a fine mesh sieve to get rid of any seeds.
Add powdered sugar to a small bowl and start by adding the berry puree, tablespoon by tablespoon, until the glaze is your desired consistency. Spread glaze over cooled blondies and serve.