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For the cake: Position the racks to divide the oven into thirds and preheat the oven to 325 degrees.
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Butter and flour three 9-inch round, 2-inch deep cake pans, flour the insides and tap out the excess.
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Whisk together the flour, cinnamon, baking powder, baking soda and salt and set aside.
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In another bowl, stir together the carrots, chopped nuts, coconut and raisins.
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Working in a mixer fitted with the paddle attachment, or in a large bowl with a whisk, beat the sugar and oil together until smooth.
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Add the eggs one by one and continue to beat until the batter is even smoother.
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If you are working in a mixer, reduce the speed to low, if you're working by hand switch to a large rubber spatula, and gently stir in the flour mixture mix only until the dry ingredients disappear.
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Just as gently, stir in the chunky ingredients.
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Divide the batter among the baking pans and slide the pans into the oven.
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Bake the cakes for 40 to 50 minutes, rotating the pans top to bottom and front to back at the midway point.
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The cakes are properly baked when a knife inserted into the centers of the cakes comes out clean; the cakes will just start to come away from the edges.
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Transfer the pans to cooling racks, cool for 5 minutes, then turn out onto racks to cool to room temperature.
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(At this point, the cakes can be wrapped airtight and kept at room temperature overnight or frozen for up to 2 months; thaw before frosting.)
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For the frosting: Working in a mixer fitted with the paddle attachment, beat the cream cheese and butter together until smooth and creamy.
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Gradually add the sugar and continue to beat until the frosting is velvety smooth.
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Beat in the lemon juice or extract.
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If you'd like to have coconut in the filling, scoop out about 1/2 of the frosting and stir the coconut into this portion.
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To frost the cake, place one layer of the cake, right-side up, on a cardboard round or a cake plate.
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If you've added coconut to the frosting, use half of coconut frosting to generously cover the first layer.
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Use an offset spatula or a spoon to smooth the frosting all the way to the edges of the layer.
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Top with the second layer, this time placing the cake top-side down.
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Frost with the remainder of the coconut frosting.
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Top with the last layer, right-side up and use the plain frosting to cover the top and the sides, if you want of the cake.
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Finish the top layer with swirls of frosting.
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If you want to top the cake with toasted nuts or coconut, sprinkle on these ingredients now, while the frosting is soft.
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Slide the cake into the refrigerator for 15 minutes, just to set the frosting.
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Serving: The cake can be served as soon as the frosting is set.
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It can also wait, at room temperature and covered with a cake keeper, overnight.
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The cake is best served in thick slices at room temperature and, while it's good plain, it's better with whipped cream, vanilla ice cream or even some lemon curd with a little whipped cream folded in.
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Storing: Covered the cake will keep at room temperature for 2 to 3 days.
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It can also be frozen, uncovered, and then, when it is firmed, wrapped airtight and kept in the freezer for up to 2 months; defrost, still wrapped, in the refrigerator overnight.
