Use a juicer or reamer to extract fresh lemon juice from the lemons, aiming for about 1 cup of juice. Strain out any seeds or pulp for a smooth, bright yellow liquid.
Place the raspberries in a bowl and gently muddle them with a muddler or the back of a wooden spoon until they release their deep color and tangy aroma, creating a somewhat thick, crushed mixture.
Pour the muddled berries through a fine sieve or strainer into a large pitcher, pressing gently to extract the vibrant, slightly thick syrup and catch any seeds or pulp.
Add the superfine sugar to the raspberry syrup in the pitcher and stir until fully dissolved. The syrup should become glossy and slightly thickened as the sugar dissolves.
Mix in the freshly squeezed lemon juice into the pitcher, whisking gently to combine all the bright flavors and aromas.
Pour the cold water into the pitcher and stir well, diluting the syrup into a refreshing lemonade base. Taste and adjust sweetness or acidity if needed.
Fill glasses with crushed ice and pour the raspberry lemonade over, allowing the fizzy bubbles to rise as you serve.
Optionally, garnish each glass with a sprig of fresh mint and serve immediately to enjoy the bright, bubbly refreshment.