In a saucepan, over low heat, combine ginger, lemon juice, lemon peel, and sugar.  Simmer for about 20 minutes, or longer if you want your syrup to be more concentrated. 

Remove from heat and put the syrup through a strainer, so the pieces of ginger and lemon peel are disregarded. 

Store the syrup in a mason jar or another container.  Let syrup cool before adding it to any drinks. 

Make each glass of ginger ale at a time.  Add a few tablespoons of syrup to 16 ounces of fizzy water and stir.