Using a serrated cake or bread knife, carefully cut the top 1-inch from the cake. Carefully remove and set aside. Using the tip of the knife, cut into the cake along the inner and outer edges, leaving a 1-inch border of cake intact. Using your fingers, carefully hollow out the cake between the two cuts, leaving an empty "tunnel". Tear the removed cake into bite-size pieces and set aside.
In a large mixing bowl using an electric mixer, beat the cream cheese until light and fluffy. Add the condensed milk and beat until thoroughly combined. Stir in lemon juice and 2 teaspoons of the liqueur. Gently fold in the cake pieces and strawberries. Spoon the mixture into the tunnel in the center of the hollowed out cake, and cover with the reserved cake top. Cover cake with plastic wrap and refrigerate at least 8 hours or overnight.
When ready to serve the cake, whip the cream until it begins to form peaks Add the confectioners' sugar and remaining 2 teaspoons of liqueur. Whip until the cream forms stiff peaks but is not dry. Frost the cake with the whipped cream and decorate with reserved whole strawberries. Refrigerate for up to 1 hour, or serve immediately.