In a small bowl place strawberries, lemon juice, and 1/3 cup of sugar.
Mix together and place in the fridge to allow the strawberries to macerate for 2 hrs.
In a medium bowl of a mixer combine the remaining 2/3 cup sugar, milk, and vanilla together.
Mix at a medium speed until sugar is dissolved.
Place freezer bowl on the ice cream machine.
Place the paddle in the freezer bowl and pour in mixture.
Add in the 2 cups of heavy cream and place the top of the ice cream mixture on.
Turn the ice cream maker on.
Let the maker churn for 25 minutes.
Add the strawberry mixture into the ice cream maker freezer bowl and continue to churn for an additional 5 minutes.
Turn off ice cream maker and put the ice cream into a freezer safe container and let it ripen for 2 hours.