Preheat oven to 350°F (175°C). Combine finely ground pistachios, graham cracker crumbs, sugar, and melted butter. Press mixture into the bottom of a 9-inch springform pan and bake for 10 minutes. Cool completely.
Beat cream cheese with sugar until smooth. Add eggs one at a time, blending well after each addition. Mix in heavy cream, lemon juice, lemon zest, and vanilla extract. Pour over cooled crust.
Bake the cream cheese layer for 25 minutes. Allow to cool, then chill in the refrigerator for 1 hour.
Combine raspberry puree, sugar, and dissolved gelatin. Carefully fold in whipped heavy cream to create mousse. Spread mousse evenly over chilled lemon cream cheese layer.
Refrigerate the layered cheesecake until the mousse is set, about 2 hours.
Before serving, decorate the cheesecake with fresh raspberries, whipped cream, crushed pistachios, raspberry coulis, and lemon zest.