Preheat the oven to 350 degrees. Line 3 large cookie sheets with parchment paper; set aside. Using an electric mixer, combine the butter, 1 cup sugar, the lemon peel and juice until fluffy. Mix in the egg. Add the flour, baking soda and salt and combine.
Place the remaining cup sugar in a small bowl. Roll heaping teaspoons of dough into balls, then roll in the sugar. Place on the prepared cookie sheets a few inches apart. Bake until golden around the edges, about 15 minutes. Transfer the cookie sheets to racks to cool completely.