In a small saucepan, combine the 3 quarts of water and the barley. Over low heat, simmer until the water has been reduced by about a third, 20 to 30 minutes. Pour through a fine sieve into a gallon pitcher or jug. In a saucepan, combine the sugar, the remaining 1 cup of water, zest, and the lemon pulp and boil until syrupy. Push the lemon mixture through a sieve, discarding the pulp that remains. Stir the lemon mixture into the barley water. Refrigerate and serve over ice.