In a small bowl, add lemon juice and chopped ginger ale. Using a muddler or the back of a spoon, press the ginger to the sides of the bowl and break it apart until the lemon juice is cloudy and the consistency is like watery applesauce. It’s okay if you still have a few solid pieces of ginger. At this point, you can do one of two things: you can either add the lemon-ginger mix as-is directly to the pitcher OR you can strain the lemon-ginger mixture to remove any of the solid pieces. If you use a strainer, use the muddler or the back of a spoon to press the pieces against the strainer so that you get all the juice out. Add the juice to the pitcher and discard anything that’s left in the strainer.