Combine eggs, sugar, and half-and-half or light cream in a heavy medium saucepan. Cook and stir over medium heat about 12 minutes or until thickened and bubbly. Cover and chill mixture for 1 hour.
Beat cream cheese until smooth. Gradually beat in the cooled egg mixture. Stir in lemon juice and vanilla. Stir in whipping cream.
Freeze in a 4- or 5-quart ice cream freezer according to the manufacturers directions. When mixture is frozen, remove the dasher and stir in the strawberry ice cream topping with a long handled spoon until marbled but not thoroughly mixed. Makes about 3 quarts.