Preheat your oven to 350ºF. Grease a 9-inch pie plate and set aside.
Mix together 1 3/4 cups graham cracker crumbs and 3 tablespoons sugar. Add 1/3 cup melted butter until combined. Pat into the pie plate and bake for 8 minutes until golden. Cool completely.
Make the ice cream base by beating together sugar, cream cheese, vanilla, and an egg until smooth. Heat milk in a saucepan until almost boiling.
Pour hot milk into the cream cheese mixture while whisking. Then pour back into the saucepan and cook over medium heat until thickened.
Remove from heat, cool to room temperature, then add lemon juice and lightly whipped cream.
Chill the mixture in the refrigerator. Freeze according to your ice cream maker instructions. Once firm, scoop into the crust.
Freeze the pie until firm enough to cut, about an hour. Mix strawberries with sugar to taste, let rest, and serve on top of slices.