In either a stand mixer fixed with a paddle attachment or using a hand held electric mixer, cream the cream cheese until light and fluffy, about 3 to 5 minutes. Slowly add the milk mixing on low speed until well combined. Stir in the lemon juice and vanilla and pour into the crust. Place the pie into the refrigerator for at least 2 hours up to overnight, until well chilled and set.
Top the pie with the pie filling just before serving.