Preheat the oven to 375°F (190°C). Coat a 15x10x1-inch (38 cm x 25 cm x 2.5 cm) baking pan with nonstick spray, line it with parchment paper, and spray the parchment again with nonstick spray; set aside.
In a bowl, stir together the flour, cinnamon, baking powder, ginger, salt, and nutmeg; set aside.
In a stand mixer, beat the eggs on high speed for 5 minutes. Gradually add the sugar on medium speed until combined. Mix in the pumpkin and lemon juice. On low speed, beat in the flour mixture until just combined. Spread the batter evenly in the prepared pan and sprinkle with walnuts.
Bake for 15 minutes, or until the cake springs back when lightly touched. Loosen the edges of the cake from the pan and turn it out onto a clean kitchen towel sprinkled lightly with powdered sugar. Remove the parchment paper. Roll the towel and cake into a spiral, starting from a short side, and let it cool on a wire rack.
Create the filling by beating the cream cheese, butter, and vanilla extract on medium speed in a stand mixer until smooth. Gradually beat in the powdered sugar until well combined.
Unroll the cake and remove the towel. Spread the filling over the cake, leaving a 1-inch (2.5 cm) unfrosted border. Roll the cake back up and trim the ends. Cover with plastic wrap and chill for a minimum of 2 hours.
Notes
For the cleanest cut, slightly freeze the cake before slicing and serving.