Preheat oven to 350 degrees. Grease and flour 2 loaf pans or line with parchment. NOTE: I highly recommend the parchment. I had one loaf completely fall apart on me.
Mix the flour, baking powder and salt thoroughly in a large bowl and sift together. Set aside.
In the bowl of a stand mixer, using the whisk attachment, beat the sugar, lemon olive oil, lemon zest, and vanilla on high speed until well blended. Add the eggs one at a time; beating well after each addition. Beat for 3-5 minutes until mixture is thick and pale yellow.
In a small bowl, combine the soy milk and sour cream. Stop the mixer and pour in half of the soy milk mixture. Beat until blended. Repeat with half of the flour, followed by the remaining soy milk mixture and then the remaining flour. Scrape the batter into the two loaf pans.
Bake for 50–60 minutes or until a skewer comes out clean. Cool the pans on a rack.