Preheat the oven to 350°F. Prepare two 9-inch cake pans. Cut out rounds of parchment paper and place in the bottoms of the pans. Butter the rounds and the sides of the pan.
Sift the dry ingredients into a bowl. Add the oil, eggs, and vanilla. Mix just until the dry ingredients are moistened. Fold in the chopped walnuts, coconut, carrots, and pineapple.
Pour the batter into the prepared pans. Set on the middle rack of the oven and bake at 350°F for 45 to 50 minutes (shift positions of cakes front-to-back if necessary about halfway through), until the edges have pulled away from sides and a toothpick or sharp knife tip inserted into the center of the cakes comes out clean.
Remove the cakes from the oven and set on wire racks until cooled completely.
While the cake is cooling, make the frosting. In a stand mixer with a paddle attachment or using a hand mixer, beat together the cream cheese and butter until creamy. Slowly sift in the powdered sugar and beat until the mixture is free of lumps. Stir in the vanilla and lemon juice.
Once the cakes have cooled, remove from the pans and frost. Sprinkle the top with chopped walnuts or arrange walnut halves in a crown around the top. Serve.