Make candied lemon peels:

1. Quarter lemons lengthwise and remove peel (including white pith) in 1 piece from each quarter. I did this by carving the flesh out with a paring knife and then I used a spoon to scoop out the leftover flesh. Fruit can be set aside for another use.
2. Cut the peel into approximately 1/4 inch squares or for other uses 1/3-inch-wide-strips.
3. Put the peel in a large bowl and cover with cold water, then soak 1 hour. Drain in a colander.
4. Blanch peel: transfer peel to a medium sized heavy pot. Cover the peel by 1 inch in cold water and bring to a boil. Reduce heat and simmer 10 minutes, then drain in a colander. Repeat 2 more times.
5. Cover with cold water one more time and bring to a boil. Simmer for 30 more minutes, then drain in a colander.
6. Return pot to stovetop and add 4 cups sugar and 6 cups water. Bring to a boil, stirring until sugar is dissolved. Boil until syrup registers 220°F, about 30 minutes.
7. Add peel and simmer over low heat until translucent, about 45 minutes. Remove from heat and let peel stand in syrup, uncovered, at room temperature 8 to 12 hours.
8. Return syrup with peel to a boil and boil, uncovered and undisturbed, until it registers 226°F on a thermometer, about 30 minutes. Remove from heat and let stand uncovered another 8 to 12 hours.
9. Return syrup with peel to a boil one more time, uncovered and undisturbed, until it registers 228°F on a candy thermometer, about 30 minutes. Remove from heat and let peel and syrup stand uncovered, at room temperature for 8 to 12 hours.
10. Reheat syrup with peel over low heat (careful as it will burn!) until the syrup has liquefied (peel will have absorbed most of the syrup), then drain peel in a colander, catching liquid contents in a bowl or pot as they may clog your drain!
11. Immediately spread peel, separating pieces, on baking racks set onto cookie sheets and dry, uncovered, 8 to 24 hours. If they continue to be a bit sticky, you can bake them at 165F for 15-25 minutes.

Assemble the appetizer:

1. Cut the figs crosswise into 1/4 inch slices, discarding top and bottom slice.
2. Place a dab of goat cheese on each fig slice.
3. Top each goat cheese with a piece of candied lemon and serve!