Grease a 9 inch round pan, and line with parchment paper. Preheat oven to 350 degrees F.
In a large bowl, whisk the almond flour, coconut flour, baking powder, baking soda, salt, cinnamon, and pumpkin pie spice together. Set aside.
In another bowl, whisk the olive oil, eggs, brown sugar, pumpkin puree, and vanilla extract together until combined
Pour the dry ingredients into the bowl of wet ingredients and mix until completely combined. Let the batter sit for a few minutes.
Pour the batter into the round pan and bake for 25 minutes. The cake should be golden and a toothpick should come out clean.
While the cake cools, make the cream cheese frosting. Add the cream cheese, powdered sugar, vanilla and lemon juice to a food processor and mix until smooth.
Once the cake has cooled, frost with the cream cheese frosting and serve.