In a large mixing bowl, beat the heavy cream with the sugar and vanilla on high speed with an electric mixer until stiff peaks form. This should take about 4-5 minutes.
In a blender combine the ice with condensed milk and lemon juice. Blend for about a minute.
Add in all of the whipped cream from the bowl and then blend again until well combined and no large ice chunks remain.
Divide the drink between 4 tall glasses and serve.