Place the lemon slices, raspberries, and sugar in a large mixing bowl. Set the bowl over paper towels or newspapers as this step is fairly messy; a great outdoor activity! Using a wooden spoon, pound the lemon slices and raspberries for several minutes until all the juice has been extracted and the sugar is mostly dissolved. Make sure to press the lemons thoroughly to get all the good juice out.
Strain the lemon, raspberry mixture through a fine-mesh sieve into a pitcher to remove all the seeds. To make a pitcher of cordial, add 4 to 6 cups of cold water to the raspberry syrup, or make individual glasses by adding about 1/4 cup of raspberry syrup for every 1 cup of water. Serve cold over ice.
Serving Size 1 cup