Preheat the oven to 165°C/fan 145°C/gas mark 3. Grease a 20 cm fluted ring tin.
Whisk the aquafaba in a bowl with an electric whisk, or using a standmixer until stiff. Continue whisking and gradually add the caster sugar, then whisk until stiff and glossy. Add the xanthan gum and whisk for a further 3 minutes.
Soften the butter and beat until creamy. Add the lime zest and half of the lavender. Beat in the aquafaba in 3 stages. Mix the flour and baking powder together, then fold into the butter mix until just combined.
Scrape the batter into the prepared ring tin and bake for 25-30 minutes until a skewer inserted into the centre comes out clean. Prick the surface of the cake all over with a skewer, to create ‘channels’ for the syrup.
Allow to cool in the tin for 15 minutes, then turn the cake out.
Put the rest of the lavender flowers, lime zest and juice and caster sugar in a small saucepan with 1 tablespoon of water. Bring to the boil for 3 minutes, then gently pour over the cake. Sprinkle with the demerara sugar and extra lavender flowers and allow to cool.