Preheat the oven to 350 degrees F.
Oil and flour a 9-inch springform pan or a bundt pan.
Mix the flour, baking powder, baking soda and salt in a bowl.
Put the oil, sugar and applesauce in a large bowl or the bowl of a stand mixer and beat on medium speed for two minutes. Scrape down the bottom and sides of bowl, then add the lemon juice, zest, vanilla, apple cider vinegar and milk.
Add the flour to the milk-oil mixture in two batches, mixing for no more than 20 seconds after each addition. Scrape down the sides of the bowl with a spatula to make sure everything's mixed.
Remove the bowl from the mixer and stir in the blueberries. You can toss the blueberries with a tablespoon of flour first if you want to make sure they don't sink to the bottom of the cake. I didn't coat them and they didn't sink.
Pour the batter into the prepared cake pan, place the pan on a baking sheet, and bake for 45-55 minutes or until a toothpick in the center comes out clean.
Remove the cake pan to a rack and let it cool in the pan for 10 minutes before unmolding. If using a bundt pan, unmold by placing a plate over the mouth of the pan and flipping in a quick motion.