Use a paper towel to wipe bottom and sides of loaf pan with coconut oil. Lightly coat with flour. Set aside.
Use a microplane to zest the lemons, scraping off the yellow skin of the lemon, just exposing the white beneath and then moving to a new area. You don't want to scrape the white, it is bitter. Place zest in a small bowl and set aside. Cut lemons in half and squeeze juice into a bowl. Set aside.
In a medium sized bowl, whisk together flour baking soda, baking powder and salt. Set aside.
In a large bowl, use a mixer to combine coconut oil and sugar, mixing for one minute, until very smooth. Beat in the eggs, one at a time, then beat in the yogurt, lemon zest, vanilla, and 1/4 cup lemon juice (reserve remaining juice for icing). Scrape down the side and bottom of the bowl, then beat in the dry ingredients, 1/3 at a time, until just incorporated. Using a rubber spatula to gently fold in the raspberries.
Pour batter into prepared loaf pan. Bake until a toothpick inserted in the center of the cake comes out clean, about 1 hour and 15 minutes. Transfer the pan to a rack and let the cake cool completely, about 1 hour.