Place a rack in the center of the oven and preheat oven to 180ºC (350ºF). Line a 8-inch/20 cm square cake pan with parchment paper. Lining it makes it easier to remove the brownie once it is baked.
Start by melting the vegan butter and the white chocolate pieces in a heatproof bowl over a pan of simmering water. Alternatively, you can put the butter and chocolate in a microwave-safe bowl and microwave until melted and smooth, about 2 minutes, stirring every 30 seconds with a rubber spatula. Do not over heat as chocolate burns easily. Let it cool down.
In a large bowl, mix the apple sauce and the coconut sugar until combined. Add the butter and the molten chocolate and mix well. Stir in the zest of one lemon, the lemon juice, the flour and the baking powder, and blend until all is incorporated. Do not over mix.
Spread the mixture into the prepared pan and bake for 25 minutes. Check for doneness inserting a skewer in the center, it should come out clean or almost clean. Don't cook it for longer, it continues to cook until set, as it cools.
Remove from the oven. Place the pan on a wire rack and let it cool for 30 minutes or until cold enough to handle. Using the edges of the parchment paper, lift the cooled brownie out of the pan, and let it cool completely on the wire rack.
For the Lemon Glaze
Stir the powdered sugar together with the lemon juice until a smooth consistency is reached.
Pour the glaze over the brownie. Use a knife or a spatula to spread it to the edges of the brownie. Once the glaze has hardened, cut the brownie into 16 squares.