In a small bowl, combine 1/3 cup sugar, strawberries, and lemon juice; gently stir.  Allow the strawberry macerate for 1 to 2 hours.

In a medium bowl, mix together milk and remaining sugar with a hand mixer or, about 1 to 2 minutes until sugar is dissolved.  Stir in heavy cream, vanilla, and juice from strawberries.

Pour mixture into the bowl of an ice cream mixer and turn on the machine.  In the Cuisinart, it took about 25 to 30 minutes to thicken.  In the last 5 minutes pour in strawberries.

If desired, place ice cream in freezer about 1-2 hours before serving to allow ice cream to ripen. Yields 1 1/2 quarts.