In a large pitcher, combine the freshly squeezed lemon juice and granulated sugar. Stir until the sugar is completely dissolved.
Add the cold water to the pitcher and mix well. Set aside.
In a medium bowl, whip the heavy cream and vanilla extract using an electric mixer until soft peaks form.
Gently fold in the raspberry puree into the whipped cream until well combined, creating a pink color.
To serve, fill glasses with ice cubes and pour the lemonade mixture over the ice, leaving some space at the top.
Spoon the whipped raspberry cream on top of each glass of lemonade.
Garnish with lemon slices and fresh raspberries, if desired.