For the icebox cake: In a large bowl, using an electric mixer on high speed, beat together the cream, sugar and vanilla until soft peaks form. Transfer to a large resealable freezer bag or a pastry bag fitted with a large round tip. (If using a freezer bag, snip off a corner when ready to pipe.)
Arrange an even layer of cookies in a 9-inch springform pan (or on a large flat plate). Spread the cookies with a 1/4-inch layer of whipped cream, leaving a narrow border at the edges. Repeat with the remaining cookies and cream; there should be 7 to 8 cookie layers total. End with a layer of whipped cream and then pipe cream on top in concentric circles to simulate a bumpy cake. Cover with plastic wrap and refrigerate overnight.
For the cherry sauce: Bring the cherries, sugar and 2/3 cup water to a boil in a medium saucepan over medium-high heat, stirring often. Stir together the cornstarch and 1/4 cup water in a small bowl until smooth. Stir the cornstarch slurry into the boiling cherry mixture. Return to a boil and cook until thickened, stirring constantly, about 1 minute. Remove from the heat and stir in the lemon juice. Puree in a blender or with an immersion blender.
To serve, dust the top of the icebox cake with cocoa powder and drizzle with cherry sauce.