In a blender or food processor combine the raspberries, warm water and granulated sugar. Blend until pureed. With a bowl underneath to collect the mixture, pour the raspberry mixture into a fine mesh sieve. Use the back of a spoon to press the mixture into the sieve to remove as much liquid as possible, you should get about 1/4-1/3 cup raspberry liquid. Set aside.
Juice the lemons. With a bowl underneath to collect the mixture, pour the lemon mixture into a fine mesh sieve. Use the back of a spoon to press the mixture into the sieve to remove as much liquid as possible, you should get about 1& 1/2 cups lemon juice.
In a large pitcher combine the lemon juice, raspberry juice and cold water. Taste and add more water if needed.
Notes
You can use fresh or frozen raspberries. If using frozen raspberries, thaw them first.How to store: Store leftover lemonade in a covered pitcher for 3 to 4 days; give it a good stir before serving.