Place a rack in the middle of the oven, then preheat it to 180 °C / 350 °F. Line a large baking sheet with parchment paper.
Beat butter (room temp), coconut oil, sugar, and vanilla using an electric mixer. Mix for 1 - 2 minutes at medium speed until the mixture is creamy and combined. Add in the egg and grated lemon zest and continue mixing until combined. Add the ground almonds, whole wheat flour, all-purpose flour, and baking powder. Mix until combined.
shape into cookies and bake
Shape the cookie dough into 24 small balls, each weighing approx. 14g (0.5 ounces). Place the cookie balls onto the prepared baking sheet, leaving enough space for expansion. Place in the preheated oven and bake for 10 - 12 minutes at 180 °C / 350 °F. Set the baked cookies aside to cool to room temperature.
While the cookies bake, make the lemon poppy seed icing. Combine lemon zest, poppy seeds, icing sugar, and lemon juice in a bowl until smooth. Dip half of the cookie top in the prepared icing and set aside for the icing to set. Serve or store.