Preheat the oven to 350°F. Prepare a muffin pan with liners or a coating of nonstick spray.
In a large mixing bowl, combine the softened butter and granulated erythritol. Mix in the eggs, lemon juice, lemon zest, vanilla, and coconut milk.
In a separate bowl, combine the almond flour, salt, and baking powder. Add the dry ingredients to the wet mixture and stir until combined. Fold in the blackberries.
Divide the batter evenly among the cavities of the prepared muffin pan.
Bake until a knife inserted into the center of a muffin pulls out clean, about 20 minutes.
Remove from oven and let muffins rest in the pan for about 15 minutes. To make removing muffins from the pan easier, run a knife around the edges of each cavity. Transfer muffins to a wire cooling rack. Serve warm, at room temp, or chilled.