In a small bowl, combine the strawberries with the lemon juice and 1/2 cup of the sugar. Stir gently and allow the strawberries to macerate in the juices for 2 hours. Strain the berries, reserving juices. Mash or puree half the berries.
In a medium mixing bowl, use a hand mixer on low speed to combine the milk and remaining granulated sugar until sugar dissolves, about 1 to 2 minutes.
Stir in the heavy cream, reserved strawberry juice, mashed strawberries and vanilla.
Turn the ice cream machine on; pour the mixture into freezer bowl, and let mix until thickened, about 20 to 25 minutes.
Five minutes before mixing is completed, add the reserved sliced strawberries and let mix in completely.
The ice cream will have a soft, creamy texture. If a firmer consistency is desired, transfer the ice cream to an airtight container and freeze for several hours. Remove from freezer about 15 minutes before serving.If you'd prefer not to have large strawberry slices in your ice cream, dice them into very petite pieces or puree all the strawberries.