Position rack in center of oven and preheat to 350 degrees F.
Spray 1 half-sheet pan with nonstick cooking spray. Line bottom of pan with parchment paper; spray paper. Sift flour and next 6 ingredients into medium bowl. Mix in crystallized ginger. Using an electric mixer, beat butter in large bowl until fluffy. Beat in brown sugar. Beat in eggs, 1 at a time. Gradually beat in molasses, followed by 1 cup boiling water. Mix in grated lemon peel. Gradually mix in dry ingredients. Transfer batter to prepared pan. Bake until a tester inserted into the center of the cake comes out clean, about 20 to 25 minutes. Transfer to a rack to cool for 15 minutes. Run a knife around the pan sides. Turn out onto a rack and peel off paper. Cool and cut into 1-inch cubes.
Using a trifle bowl, start with an even layer of gingerbread cubes, top with 1/3 of the lemon curd mixture, and 1/3 of the blackberry sauce. Repeat 2 more times. Top with remaining whipped cream. Cover and refrigerate for at least 4 hours or overnight before serving.
Place lemon curd in a large bowl. Fold in half of the whipped cream until combined. Refrigerate if not using immediately. Reserve remaining whipped cream for the top of the trifle.
Place blackberries, sugar, and salt in a medium saucepan and cook until the berries are soft and the sugar has melted. Transfer to a blender and blend until smooth. Pour through a strainer into a bowl. Stir in the framboise and lemon juice. Set aside until ready to use.