With a vegetable peeler, remove zest from each lemon in a long, continuous spiral. Juice lemons, and strain pulp (you should have 3/4 cup juice). Set aside.
Heat sugar and 1/2 cup water in a small saucepan over medium-high heat, stirring until sugar has dissolved. Bring to a boil. Remove from heat. Add zest. Let syrup cool completely, about 2 hours.
Pour Champagne, vodka, lemon juice, and syrup into a punch bowl; stir. Serve glasses of punch with candied peels.
Lemons are easier to peel and will release more juice at room temperature than when chilled.