Process the carrot cake ingredients. Add the walnuts to a food processor bowl fitted with an S blade and process until the nuts are finely ground but still have some texture. Add the dates, shredded coconut, lemon juice, lemon zest, vanilla extract, and spices to the food processor and process until all the ingredients begin to stick together. Lastly, using a spatula, fold in the coconut flour and carrots.
Press the mixture into a springform pan. Divide the carrot cake mixture in half. Transfer the first half of the mixture to a lightly greased 6-inch/15-cm springform pan (if you're using anything other than a springform pan, line it with parchment paper for easier removal), and press it into an even layer. The top of the cake should be smooth and leveled. Transfer the cake to the freezer to firm up, for 10-15 minutes. Repeat with the other half of the cake mixture. Note: if you only have one 6-inch/15-cm springform pan, let the first layer of cake chill first. Then carefully remove the cake from the pan, transfer it to a round cake board, and place it back into the freezer. Clean the springform pan, grease it once again, and repeat the steps above with the other half of the carrot cake mixture. Blend the carrot cake frosting ingredients. Add the cashews, coconut milk, coconut oil, maple syrup, lemon juice, and vanilla extract to a high-speed blender, and blend on high until smooth and creamy.
Assemble the cake. With the carrot cake layer still in the springform pan, pour the first half of the frosting onto the cake and tap out any air bubbles. Transfer the springform pan with the cake back to the freezer to let the frosting firm up slightly, for about 30 minutes. Then place the second carrot cake layer on top of the frosting and gently press it into the frosting to make sure it's really on there. Pour the second half of the frosting on top of the cake and tap out any air bubbles once again.
Chill. Cover the springform pan with a piece of paper towel (to trap any condensation), and then double-wrap the entire springform pan with plastic wrap for the best chance of preserving the cake's taste and texture. Transfer the wrapped cake to the freezer for at least 6 hours, ideally overnight. The more frozen the cake, the easier and cleaner the removal from the pan.
Serve. Once set, remove the carrot cake from the springform pan. Serve the cake frozen or let it thaw at room temperature for 15-20 minutes before serving.
Store. Leftover carrot cake keeps well in an airtight container in the refrigerator for up to 1 week or in the freezer for up to 1 month (ideal).