Preheat oven to 350 degrees. Wrap exterior of a 9-inch springform pan in 2 layers of foil.
On a generously floured piece of parchment, roll dough to a 13-by-10-inch rectangle, about 1/4 inch thick. Brush off excess flour. Slide dough and parchment onto a baking sheet. Bake until firm and golden brown, about 14 minutes. Let cool completely on sheet on a wire rack. Break into large pieces, then pulse in a food processor until finely ground.
Combine butter, 1/4 cup sugar, and 2 cups cookie crumbs in a bowl. Press mixture firmly and evenly into bottom and one-third of the way up sides of prepared pan. Bake until set, about 10 minutes. Let cool on rack.
Reduce oven temperature to 325 degrees. Beat cream cheese with a mixer on medium speed until fluffy, about 3 minutes. Beat in remaining 1 1/2 cups sugar and the vanilla, scraping down sides of bowl as needed. Reduce speed to low. Add eggs, 1 at a time, beating well after each addition and scraping sides of bowl as needed. Beat in molasses, salt, spices, and lemon zest. Pour filling into cooled crust.
Place cheesecake in a large, shallow roasting pan. Transfer to oven, and carefully add enough hot water to roasting pan to come about halfway up sides of springform pan. Bake until cheesecake is set but still slightly wobbly in center, 60 to 65 minutes. Carefully remove springform pan from roasting pan, and let cool on a wire rack. Refrigerate, uncovered, for at least 8 hours (preferably overnight).
Before serving, run a hot knife around edges of cheesecake to loosen, and remove sides of pan. Arrange gingerbread cookies in center of cake in a circle (with heads facing inward and arms touching, alternating light and dark).