Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a 9-inch springform pan.
Beat egg yolks and sugar together in a large bowl with an electric mixer until fluffy. Beat in carrots, almonds, lemon juice, and lemon zest.
Mix flour, baking powder, and salt together in a bowl and add to the batter. Stir well to combine.
Beat egg whites in a glass, metal, or ceramic bowl until stiff peaks form. Fold into the cake batter with a spatula. Pour batter into the prepared springform pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 40 to 50 minutes. Cool on a wire rack for 5 minutes. Run a table knife around the edges to loosen. Remove carefully and place on a serving plate or cooling rack. Let cool, about 30 minutes.
Knead marzipan until soft and pliable. Pinch off 1/5 and add a little green food coloring using a toothpick. Knead until marzipan is uniformly green. Color the remaining marzipan orange using the same method. Shape orange marzipan into 12 little carrots and make tiny indentations on top with a paring knife. Shape the green marzipan into little leaves. Stick 2 leaves to the top of each carrot with a little water.
Combine confectioners' sugar and enough lemon juice to make a thick icing. Coat cake with the icing. Place marzipan carrots on top around the edges in such a way that each piece of cake has a marzipan carrot. Let icing dry before slicing and serving.