In a medium saucepan, combine the fresh cranberries, granulated sugar, light brown sugar, water, ground cinnamon, and kosher salt. Bring the mixture to a boil over medium heat, stirring occasionally. Reduce the heat to low and simmer for about 15 to 20 minutes, or until the cranberries begin to break down slightly and thicken a bit. Remove the saucepan from the heat and leave to cool before spreading on the cheesecake. The Cranberry Compote can be refrigerated in an airtight container for up to 5 days.
For the crust:
Preheat oven to 375°F. Process the Nilla Wafers or graham crackers and sugar in a food processor to a fine crumb. In a medium bowl, combine the cookie crumbs, melted butter, and sugar. Mix until evenly moistened and well combined. Pour into a 9-inch springform pan. With your hands, press the crumbs into the bottom of the pan and about 1 inch up the sides. Bake the crust for 10 minutes. Remove the crust from the oven and set it aside to cool. Reduce the oven temperature to 325°F.
For the Filling:
Wrap a 10-inch springform pan with a large piece of aluminum paper, covering the underside and extending all the way to the top so there are no seams on the bottom or sides. Repeat with a few more sheets of foil for insurance. The foil will keep the water from seeping into the cheesecake.
In the bowl of a stand mixer, attach the paddle attachment. Place the cream cheese in the bowl and beat it on medium speed for about 1 minute until it becomes smooth and no lumps remain. Gradually add the sugar while continuing to beat the mixture. Beat for an additional 1 to 2 minutes until the mixture becomes creamy. Scrape down the sides and bottom of the bowl using a spatula to ensure all ingredients are well incorporated. Add the vanilla, lemon juice, and lemon zest to the mixture. Beat them into the cream cheese mixture until everything is well combined.
Add the eggs, 1 at a time, and continue to beat slowly until combined, scraping after each addition. Add sour cream and heavy cream. Periodically scrape down the sides of the bowl and the paddle. The batter should be well-mixed but not over-beaten. Pour the filling into the crust-lined pan and smooth the top with a spatula. Place the foil-wrapped springform pan in a large roasting pan.
Pour boiling water into the roasting pan until the water is about halfway up the sides of the cheesecake pan. Bake for 1 hour and 30 minutes to 1 hour and 45 minutes. The cheesecake should still jiggle (it will firm up after chilling), so be careful not to overcook. Let cool in the pan for 30 minutes.
Chill in the refrigerator, loosely covered, for a least 8 hours or overnight. Loosen the cheesecake from the sides of the pan by running a thin metal spatula around the inside rim. Unmold and transfer to a serving platter or cake stand. Using a spatula, spread a layer of warm Cranberry Compote over the surface. Slice the cheesecake with a thin, non-serrated knife that has been dipped in hot water. Wipe dry after each cut.