If you can't find freeze-dried berries—don't fear! This cheesecake still packs a double-raspberry punch.
Coat a 9-inch springform pan with cooking spray. In a medium bowl, whisk the flour, confectioners’ sugar, freeze-dried raspberries, if using, and salt. Stir in the melted butter. Transfer crust mixture to the pan. Using the bottom of a dry measuring cup, press the crust evenly into the bottom and 1 inch up the sides of the pan. Refrigerate until firm, about 20 minutes.
Meanwhile, arrange a rack in the center of the oven and preheat to 350°. Transfer the crust to the oven and bake until cooked through and starting to brown around the edges, about 25 minutes. Remove the crust from the oven and reduce the oven temperature to 325°. Let the crust cool while you make the filling.
For the filling, in a blender or food processor, puree the raspberries. Strain through a fine-mesh sieve to remove the seeds. Set the raspberry puree aside.
In the bowl of a stand mixer fitted with the paddle attachment, mix the cream cheese and sugar on medium speed until smooth, about 1 minute. Add the vanilla and then the eggs, one at a time, beating until smooth after each addition. Using a rubber spatula, scrape the bottom and sides of the bowl. Reduce the speed to low and add the flour and salt. Mix, occasionally scraping down the bottom and sides of the bowl, until smooth, about 1 minute. Stir 3/4 cup of the raspberry puree into the filling.
Pour the filling into the crust. Bake until the outside of the cheesecake is set and the center jiggles only slightly, 60 to 70 minutes. Turn the oven off and leave the door ajar for 1 hour. Remove the cheesecake from the oven and allow to cool at room temperature for another hour. Refrigerate until completely chilled, at least 4 hours.
For the topping, cook the remaining raspberry puree with the lemon juice and sugar over medium heat until the sauce is thick enough to coat the back of a spoon, about 5 minutes. Transfer to a container and let cool. Remove the cheesecake from the springform pan and slice. Serve with the sauce and whipped cream.