Preheat oven to 160 C (fan), 180 C/325 F and grease your bundt tin with vegetable shortening (not butter!)
Cream the butter and sugar together until light and fluffy. Add the dried lavender flowers, lemon juice and zest and beat well.
Add the duck eggs, one at a time, beating well after each addition.
Sift the flour, bicarbonate of soda and baking powder together in another bowl.
Add the flour mixture and the milk to the egg/butter mixture a spoonful/splash at a time, beating well after each addition.
Spoon into the prepared bundt tin, smoothing over the top so that the outer edges are higher than the middle.
Bake for 50 minutes to an hour. A skewer, when inserted into the centre of the cake, will come out clean.
Leave to cool, upright, for 15 minutes before turning out onto a wire rack to cool completely.
To prepare the drizzle, add enough lemon juice to the icing sugar to make a thick icing. Drizzle over the top of the cake and sprinkle with lavender flowers.