Preheat oven to 350 degrees F. Pulse graham crackers in food processor until finely ground.
Add sugar and melted butter; pulse until mixture resembles wet sand.
Press firmly into bottom and sides of a 9-inch pie dish. Bake 8 minutes. Cool completely.
Beat softened cream cheese until smooth and fluffy, about 2 minutes.
Add sweetened condensed milk; mix until combined.
With mixer on low, slowly pour in fresh lemon juice, then add zest and vanilla.
Mix until smooth. Filling will thicken as the citric acid reacts with the condensed milk.
Pour filling into the cooled crust. Smooth the top.
Cover with plastic wrap. Refrigerate at least 6 hours or overnight.
Before serving, whip cold heavy cream and powdered sugar to soft peaks. Spread over pie.
Garnish with lemon slices or mint. Slice with a sharp knife, wiping blade between cuts.