Make the strawberry sorbet: Combine the fresh strawberries, superfine sugar, ½ cup water and the lemon juice in a blender. Blend on high speed until completely smooth. Transfer to an ice cream maker and churn according to the manufacturer’s instructions until the consistency of soft serve. Transfer to a metal container and freeze until firm, at least 2 hours.

Meanwhile, preheat the oven to 350 degrees F. Spread the pound cake crumbs on a baking sheet and bake, tossing occasionally, until golden, 10 to 12 minutes. Let cool completely, then transfer to a bowl and add the freeze-dried strawberries; toss.

Line a 9-by-5-inch loaf pan with plastic wrap, leaving a 4-inch overhang. Allow half of the vanilla ice cream to soften at room temperature, then spread in an even layer in the bottom of the loaf pan. Transfer to the freezer to firm up slightly, 20 to 30 minutes. Scoop the strawberry sorbet on top, then spread in an even layer. Return to the freezer to firm up slightly, 20 to 30 minutes. Let the remaining vanilla ice cream soften slightly, then spread on top of the sorbet in an even layer. Fold the plastic wrap over the pan. Freeze until solid, at least 4 hours.

Place a serving dish in the freezer. Combine the heavy cream, confectioners’ sugar and vanilla in a medium bowl and beat with a mixer on medium-high speed until stiff peaks form, 2 to 3 minutes. Unmold the ice cream cake and turn it out onto the chilled dish, discarding the plastic wrap. Working quickly, spread the whipped cream all over the top and sides of the cake. Sprinkle the pound cake–strawberry crumbs on top. Freeze until the whipped cream is firm, about 1 hour.