Make the strawberry swirl. Combine the strawberries, granulated sugar, and cornstarch in a small saucepan over medium heat. Cook the strawberries for 5 minutes or until the mixture creates a sauce and is thickened. Remove from the heat and let cool completely.
Make the graham cracker crumble. Stir together the graham cracker crumbs, melted butter, brown sugar, and salt in a medium bowl. Set aside and let cool.
Make the ice cream base. Beat the cream cheese in a medium bowl until smooth and creamy. Add the sweetened condensed milk, vanilla, salt, lemon juice, and lemon zest and beat until smooth.
In separate large bowl, beat the heavy cream to soft peaks. Fold into the cream cheese mixture until combined.
Pour half of the ice cream base into the bottom of a metal pan. Top with half of the strawberry swirl and half of the graham cracker crumble. Repeat the process with the remaining ingredients.
Using a knife, swirl the layers together. Cover and freeze for 8 hours or until the ice cream is firm.