Preheat oven to 400 degrees F. Grease a baking sheet.
Sift together the flour, baking powder, baking soda, salt, sugar, lemon zest. Cut in butter with a fork or a pastry cutter until the butter is mix in well. Cut in the cream cheese.
Mix the cream, egg, and lemon juice until combined. Add the wet ingredients to the flour mixture and mix just until it come together in a ball.
On a floured surface knead the dough a couple of time. Form a 8 inch circle, with a pizza cutter or a sharp knife cut the circle into 8 wedges. Place the wedges on the prepared baking sheet about 2 inches apart. Place in a preheated oven and bake for 14 to 16 minutes. Remove from oven and remove the scones form the baking sheet onto a cooling rack. Cool completely.
While the scones are cooling prepare the icing. Mix the powder sugar gradually with the lemon juice until you have the right consistency. Drizzle over cooled scones.