Cover the rind with hot water and boil for 5 minutes. Drain.
When cool, cover with a brine of 1 quart of water and 1/4 cup of salt. Set aside for at least 6 hours.
Drain and rinse several times, and then cover the rind with fresh water and simmer until the rind is tender. Drain.
In a saucepan, place 2 cups sugar, the remaining 1 1/4 cups of water, and the lemon peel.
Cook until a drop forms a soft ball in cold water.
Add the rind. Simmer, stirring and lifting the rind from the bottom of the pan to prevent it from scorching.
Cook until the rind is clear, and the syrup forms a long thread. remove the rind and drain.
Discard the lemon peel if desired. Drop each piece of rind in sugar for coating and shake off the excess. Lay the rinds separately on a rack to cool and dry.
Notes: Do not use very small melons for this recipe as their rinds are too thin.