Place the strips of watermelon rind in a saucepan and cover with hot water. Bring to a boil over medium-high heat. Let cook at a boil for 5 minutes. Drain the rinds well and let them cool.
Meanwhile, combine 1 quart of water with the salt in a glass or plastic bowl. Mix well. When the watermelon rinds are cool, place them in the salt brine. Cover the bowl and let the rinds sit in the brine for at least 6 hours.
Drain the brine and rinse the rinds several times in fresh water. Place the rinds in a saucepan and cover with fresh water. Bring to a boil over medium-high heat and cook, stirring occasionally, until the watermelon rinds are tender.
In another saucepan, combine the sugar, lemon peel, and the remaining water. Bring to a boil over medium-high heat. Cook until the mixture reaches softball stage, about 235 degrees F on a candy thermometer.
Add the rinsed rind to the sugar mixture. Cook at a simmer, stirring frequently, until the rind is clear and the syrup forms long threads when drizzled from a spoon.
Remove the rind from the sugar mixture and let drain on a rack over waxed paper.
Place sugar in a shallow bowl. Dredge the rinds in the sugar, coating completely. Shake off any excess sugar. Place the rinds on a rack to cool and dry. When dry, store the watermelon candy in an airtight container.
