Peel lemons, and scrape white pith from rind. (Reserve lemons for other uses.) Cut rind into 1/4-inch strips.
Simmer lemon peels in salted water to cover 20 minutes. Drain. Rinse with cold water, and drain on paper towels.
Combine 1 cup sugar and 1/2 cup water in a heavy saucepan. Bring to a boil over medium heat, and stir constantly until sugar dissolves. Cook until syrup registers 234° (soft ball stage) on a candy thermometer (about 5 minutes). Add lemon peel. Cook, stirring occasionally, 15 to 20 minutes. If lemon peel begins to brown, immediately remove from heat.
Remove peels from syrup with a wooden skewer, one piece at a time, and roll in remaining 1/2 cup sugar. (Candy is very hot; do not touch.) Arrange in a single layer on a wire rack, and dry 4 to 5 hours. Store in an airtight container.