Make the Candied Lemons at least 24 hours before you plan to serve the cake. Slice the lemons into rounds as thinly as possible, remove the seeds and discard the ends. In a 12-inch skillet, heat the sugar and water over medium-low heat. Once the sugar dissolves, add the lemon slices and simmer over low heat for 30 to 40 minutes. The lemon rind should be translucent. Remove the lemon slices and place them on a baking sheet lined with parchment paper. Save the leftover lemon syrup in a jar and use it for pancakes, cocktails or tea. It will last for 2 months in the refrigerator. Let the lemon slices dry, uncovered, for 24 hours. They will firm up slightly but will remain sticky. 

Preheat the oven to 400°. Wash the beets and wrap each in foil; place on a baking sheet and roast them for about 1 hour or until they are easily pierced with a fork. Remove from the oven and let them steam for about 10 minutes in the foil. Remove foil from beets, let cool enough to handle and then carefully peel. Reduce oven temperature to 350°. 

Place the peeled beets in a food processor and blend for about 1 minute, until as smooth as possible. Measure 1 cup of the beet mixture and discard the rest or save for another use. Return the cup of beet purée to the blender, add the lemon juice and blend for 1 minute. Add the oil, butter, buttermilk and sugar. Process until smooth. Add the eggs and vanilla and process a few seconds, until just combined. Mix the remaining dry cake ingredients in a large bowl. Fold in the beet mixture and stir until no dry bits remain. 

Cut out three circles of parchment paper to fit the bottoms of three 8-inch round cake pans. Grease the sides with cooking spray. Divide the batter evenly among the three pans. Bake for 20 to 25 minutes or until a toothpick comes out clean when inserted in the center. Allow the cakes to cool in the pans for 5 minutes, then carefully flip them over onto cooling racks. Allow to cool completely. 

To make the frosting, beat the goat cheese, cream cheese and butter with an electric mixer on high for 2 to 3 minutes until fluffy and fully combined. Add the powdered sugar and vanilla, beating on low for 30 seconds and then on high for 1 more minute, until it’s smooth and fluffy. 

When the cakes are completely cooled, slice a thin layer off the top of each cake with a long, serrated knife to flatten the top. Place one cake on a plate or cake stand. Spoon a scant of the frosting onto the cake and smooth out to cover the top, avoiding the sides. Place the second cake on top of the first and repeat. Place the final cake on top and smooth the remaining frosting on the top and lightly around the sides. Avoid covering the sides completely; the layers should be visible. Decorate with the Candied Lemons (they will stick easily to the frosting) and toppings of your choice. Store leftovers in the refrigerator and consume within 2 to 3 days.