To make the syrup: Stir the sugar, water, lemon juice, and if using, the corn syrup, cinnamon sticks, and/or cloves over low heat until the sugar dissolves, about 5 minutes. Stop stirring, increase the heat to medium, and cook until the mixture is slightly syrupy, about 5 minutes (it will register 225 degrees on a candy thermometer). Discard the cinnamon sticks and whole cloves. Let cool.