Working with a stand mixer, preferably fitted with a paddle attachment, beat the sugar and oil together on medium speed until smooth. Add the eggs one by one, and continue to beat until the batter is even smoother. Reduce speed to low and add the flour mixture, mixing only until the dry ingredients disappear. Gently mix in the chunky ingredients. Divide the batter among the baking pans.
Bake for 40-50 minutes, rotating the pans from top to bottom and front to back at the midway point, until a thin knife inserted in the center comes out clean. Transfer cakes to cooling racks and cool for 10 minutes, then unmold them, and cool to room temperature.
Make the frosting: Working with a stand mixer, beat the cream cheese and butter together until smooth and creamy. Gradually add the sugar and continue to beat until the frosting is velvety smooth. Beat in lemon juice.
Assemble the cake: Put one layer top side up on a cardboard cake round or a cake plate protected by strips of wax paper. Cover the layer generously with frosting, using an offset spatula to smooth it all the way to the edges of the layer. Top with the second layer, this time placing the cake top side down, and frost with more frosting. Top with the last layer, right side up, and frost the top (and the sides, if you want) of the cake. Sprinkle with nuts or coconut, if desired. Refrigerate 30 minutes to set the frosting, before serving.