In a blender, combine cream cheese, sour cream, lemon zest, 1/3 cup granulated sugar, and a pinch of salt, and puree until completely smooth. Transfer to a bowl and chill at least 4 hours.
To make the strawberry sauce, remove stems and puree strawberries until smooth. If desired, press puree through a sieve to remove seeds.
To a small saucepan, add pureed strawberries, ¼ cup granulated sugar, and lemon juice. Heat over medium, stirring often, until sugar is dissolved and mixture is somewhat thick. Let cool completely.
To make the pretzel crumble, preheat oven to 350°F. In a bowl, combine crushed pretzels, melted butter, and brown sugar until well-mixed and crumbly. Spread mixture onto a lined baking sheet, press to flatten somewhat, and bake 7-10 minutes, until sugar has melted. Let cool completely, then break crumble into small pieces.
When ready to churn the ice cream, pour in cream cheese mixture and churn according to manufacturer's instructions.
In the last few minutes of churning, sprinkle in pretzel crumble. (You may have extra.)
Once fully churned, layer ice cream and strawberry sauce in an ice cream container or loaf pan, starting and ending with ice cream. Using a butter knife, make one or two swirls through the ice cream to marble strawberry sauce.
Cover and freeze at least 2 hours before serving.
Be sure to chill your ice cream bowl for 24 hours before churning.
Save any extra pretzel crumble or strawberry sauce for topping.