Remove tops and wash beets thoroughly. In a bowl, mix sugar, salt, vinegar, water and herbs until dissolved. Add beets and coat well. Place in a 9 " x 13 " pan, cover with foil and bake covered for 2 hours at 325°F until fork tender. Let beets cool to room temperature, then peel under cool running water. Cut into wedges and refrigerate.
Zest all three lemons; reserve zest. Juice lemons, straining out any pulp and seeds. Whisk together juice, 1 tablespoon sugar, 1 teaspoon salt and zest. Once mixed, slowly drizzle and whisk in 1/4 cup olive oil and set aside. Salad: Score 1–2 fresh pomegranates and place in a bowl of water. Break open the pomegranates under water to free the arils (seed sacs). The arils will sink to the bottom of the bowl and the membrane will float to the top. Sieve and put the arils in a separate bowl. Reserve 1 cup of the arils from fruit and set aside. (Refrigerate or freeze remaining arils for another use.) Dice the avocado. Thinly slice the bulb of fennel. Julienne 8 to 10 mint leaves. In a large bowl, combine the beets, sliced fennel, diced avocado, fresh pomegranate arils and mint. Lightly dress with the lemon vinaigrette. Transfer salad to serving plate and crumble goat cheese over the top. Serve this pomegranate recipe chilled.