Preheat the oven to 170 C / 335 F. Line the bottom of two x 9" round springform pans with parchment paper. If you only have one pan, you can bake this cake in two batches.
In a large bowl, beat together the butter and sugar-free sweetener for about a minute until fluffy.
Using medium speed, add and beat in the eggs one at a time.
Change the speed to low and mix in the vanilla, cream (or coconut cream) and lemon juice until incorporated.
Stir in the grated beetroot (make sure to squeeze out the juice first). Don't beat with a mixer as it might splash the juice all over.
Change the mixer speed to low and beat in the almond flour - 1/2 cup at a time - followed by coconut flour, cocoa powder and baking soda. Beat together until the batter is just smooth but don't over mix it.
Divide the batter between the 2 pans and flatten the top with a spatula. Bake for about 30 minutes, until an inserted toothpick comes out clean. Cool completely in the pans, then run a knife along the sides to loosen the cake. Open to release and flip to remove.
Note:If you only have one pan and want to bake it as one whole cake rather than the two layers, increase the time by 20-25 more minutes or so. Then once the sponge is cool enough, slice it into two layers. In the meantime, make the low-carb cream cheese frosting. Use a hand mixer to beat together the cream cheese and butter, until fluffy. Beat in the sweetener and vanilla, until well incorporated.
Add cream and beat again, until creamy. You can adjust the amount of cream to desired consistency. Finally, fold in a couple of tablespoons of the beet juice we reserved during prep. You can adjust the amount depending on the intensity of the colour you want.
Place one cake onto a cake stand or a plate and frost the top with 1/2 to 3/4 cup of the frosting. Place the other cake layer on top and frost the top and the side with the remaining frosting.
You can decorate the top of the cake with raspberries, strawberries, beetroot chips (you can bake your own beetroot chips even), pecans, rose petals, dried cranberries or chocolate shavings. Anything that's a darker, burgundy or brown colour will look great on top of pinkish white frosting.