Combine all of the ingredients for the cake except lemon and raspberries in a bowl. Whisk them together. Add juice and zest of 1/2 lemon and the raspberries and carefully fold them into the batter.
Preheat the oven to 180 °C. Grease the baking tin with butter and dust it with flour. Pour the batter into it and bake for approx. 45-50 minutes until done.
In the meantime, put the freeze-dried raspberries in a blender or food processor with the powdered sugar and blend until you've got a pink "dust". Set aside.
Let the cake cool down completely. Decorate with the raspberry sugar and serve!
Tipps
You can keep the raspberry sugar in a glass and decorate all of your favorite desserts and cakes with it. Of course, you can also use just powdered sugar to decorate the cake.