Preheat the oven to 180°C/350℉.
In a large bowl, whisk ½ cup (70 g/2.5 oz) buckwheat flour, 1 ½ cup (140 g/5 oz) almond flour, ½ cup (60 g/2.1 oz) arrowroot starch, 3 tbsp (23 g/0.8 oz) cocoa powder, and ¾ tsp salt. Set aside.
Make powdered xylitol by placing ¾ cup (150 g/5.3 oz) xylitol in a high-powered blender or food processor and blend on high for 30 seconds.
Using a handheld or stand mixer fitted with a paddle attachment, beat ¾ cup (150 g/5.3 oz) soft butter and powdered xylitol together on medium-high speed until combined and becomes a smooth cream light in color, about 1-2 minutes. Scrape down the sides of the bowl with a rubber spatula as needed.
Gradually add the eggs one at a time and beat on high speed until the cream doubles in volume, about 2 minutes. With the mixer on low speed, add the ½ cup (130 g/4.5 oz) natural yogurt, lemon zest, and 1 ½ tsp vanilla extract. Continue beating until everything is smooth.
Add the flour mixture, 1 cup + 4 tsp beetroot juice, 1 ½ tsp apple cider vinegar, and 1 ½ tbsp lemon juice. With a rubber spatula, mix everything slowly until combined and without pieces of flour. Lastly, add 3 tsp baking powder and fold gently.
Grease 3 baking pans and place discs of parchment paper to protect the base. Divide batter between cake pans. Bake in a preheated oven for 20 minutes. This red velvet cake has a “wet” appearance and will be baked when it is firm. Wait at least 15 minutes to unmold the pans. When the red velvet cake layers are completely cooled, frost and decorate using your imagination!