In food processor, combine strawberries, 1/3 cup sugar and lime juice; process until smooth. Chill strawberry puree in freezer for 10 minutes.
Meanwhile, with an electric mixer, in a large bowl, beat cream cheese and heavy cream and remaining 2 teaspoons of sugar to medium peaks. Reserve ¼ cup of cream mixture covered in refrigerator; fold remaining in to strawberry puree.
Divide mixture among 4 (4 oz) ramekins or foil cupcake cups. Freeze at least 1 hour or as long as overnight. Remove from freezer 10 to 15 minutes before serving. Dollop each serving with reserved cream. Garnish with fresh berries.