Begin by making the cheesecake crust: Preheat the oven to 325 degrees. Butter a nine inch springform pan. Wrap the outside of the pan in two layers of heavy duty aluminum foil.
Using the food processor, grind up the cookies into fine crumbs. Add them to the melted butter and stir until well combined. Press this on the bottom and up the sides of the pan. Bake for 15 minutes. Cool on a wire rack while you make your filling.
In an electric mixer, with the paddle attachment, beat together the cheese, sugar, vanilla, lemon juice, and lemon zest. Beat until smooth. Add the eggs and beat on low until just combined. Pour this filling into the crust.
Place the springform pan into the roasting pan and put it in the oven. Pour hot water in the pan, so that it comes halfway up the cheesecake pan. Bake for one hour, or until the cake is no longer jiggly.
Cool on a wire rack for two hours, and then cover and refrigerate for at least four hours. But, preferably, chill this overnight.
While the cake cools, make the sauce: Mix all the ingredients in a three quart saucepan. Bring them to a boil, and then simmer for 15 minutes or until the sauce is thickened. Let this chill until cold.
Remove the sides from the pan and serve the cake topped with the sauce.