Preheat the oven to 160°C (320°F) in convection mode. Grate the marzipan using a coarse mesh.
Sift the flour and baking powder together.
In a mixing bowl, beat the butter, sugar, vanilla, and lemon zest until fluffy.
Add the grated marzipan and mix on high speed.
Add the eggs one by one, mixing briefly after each addition, just until combined.
Mix in the ground almonds and lemon juice.
Gradually add the flour and baking powder mixture in portions, mixing at low speed.
Stop mixing as soon as you see some traces of flour remaining.
Finish mixing the batter with a spoon and pour it into a greased or lined cake pan.
Bake the cake for about an hour, or until a toothpick inserted comes out clean.
Allow the cake to cool completely before adding the frosting.
For the frosting, place powdered sugar in a bowl and add lemon juice in small portions, mixing thoroughly until you achieve a thick but slightly runny consistency.
Spread the icing evenly on top of the cooled cake.