Pour the heavy cream into a chilled bowl of a stand mixer that is fitted with the whisk attachment. Whip on medium speed for 5 to 7 minutes, or until stiff peaks begin to form. Set aside for later.
In a large mixing bowl, combine the sweetened condensed milk, vanilla extract, and the lime juice. Stir until combined.
Gently fold in the whipped cream until incorporated. Sprinkle the graham cracker crumbs and turn just once or twice to mix in.
Pour the mixture into a freezer safe container and freeze until solid, 4 hours or up to overnight ideally.