Preheat the oven to 350°F / 175°C. Butter and line an 8×4" loaf pan with parchment paper.
In a medium-sized bowl, whisk together the flour, baking powder, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, or with a hand mixer, beat together the butter, oil, and sugar for 5 minutes until light and fluffy.
Scrape down the sides of the bowl, and add in one egg at a time, beating until combined after the two additions.
Add in the egg white, vanilla, and sour cream and beat until combined.
Alternate between adding the flour mixture and the milk. Fold in ½ of the flour mixture, then all of the milk, followed by the rest of the flour mixture.
In a small mixing bowl, whisk together the butterfly pea powder and milk until smooth.
Add in 300g (~1 ⅓ c.) of the vanilla batter, and fold the mixture together just until fully combined.
Remove 150g (⅔ c.) of the blue batter and place it into a small mixing bowl. Mix in the lemon juice just until fully combined.
Time to layer the loaf! Pour ⅓ of the vanilla cake batter into the bottom of your prepared loaf pan, and smooth it out into an even layer.
Top with the purple cake batter and smooth, followed by ½ of the remaining vanilla cake batter.
Smooth the blue batter into an even layer on top of that, then finish off with a smooth layer of the remaining vanilla batter.
Use a knife to swirl the batter together. Bake for 50-60 minutes, until a toothpick inserted in the cake comes out clean or with only a few moist crumbs.
Allow the cake to cool in the loaf pan for at least 10 minutes before transferring it to a wire rack to cool.