Position a rack in the lower third of the oven and preheat to 325F. Grease a 9-inch springform pan or deep cake pan with the coconut oil. Line the bottom of the pan with parchment paper and grease the parchment. If using a springform pan, place on a rimmed baking sheet to catch any drips.

In a large bowl, whisk together the olive oil, 1⁄2 cup of the sugar, the lemon zest and juice, and the egg yolks. Sift in the almond flour, tapioca flour, baking powder, and salt. Whisk to combine.

In the bowl of a stand mixer fitted with the whip attachment (or in a bowl with an electric egg beater), beat the egg whites and cream of tartar on medium- high speed until foamy. With the mixer running, gradually add the remaining 1⁄4 cup sugar and whip until the egg whites are shiny and hold firm peaks when you hold the whip upside down. Fold one-third of the whipped egg whites into the batter, then fold in the remaining whipped whites. Transfer to the prepared pan and smooth the top.

Bake until deep golden on top and beginning to pull away from the sides of the pan and the top springs back when pressed lightly, 40 to 45 minutes. If the cake is darkening too quickly, tent with aluminum foil.

Let cool slightly, then loosen the edges with a small offset spatula and release the sides if using a springform pan. Invert the cake onto a wire rack, peel away the parchment, then turn right side up and let cool completely. Dust with powdered sugar, cut into wedges, and serve with cream and berries.