Place a rack in the center of the oven and preheat the oven to 350 degrees F. Line a muffin tray with paper liners and set aside.
Whisk flour, baking powder, sea salt, and baking soda in a medium bowl. No need to sift. Whisk the buttermilk and the lemon juice in a small bowl to blend. In another small bowl, combine the sugar and lemon zest and using your hands or the back of a wooden spoon mash the zest in with the sugar so the oils are released.
Using an electric mixer fitted with the paddle attachment, beat the sugar and lemon zest mixture, butter, and coconut oil. Add eggs one at a time, beating well after each addition until mixture is light and fluffy. Occasionally scrap down sides of bowl. Beat in dry ingredients in 3 additions alternating with the buttermilk mixture in 2 additions. Mix just until blended. No not overmix. Mix in poppy seeds. Spoon batter into prepared muffin cups about three-fourths of the way full.
Bake muffins for 20 - 22 minutes or until a toothpick inserted in the center comes out clean. Let cool in pan 5 minutes prior to transferring to a wire rack.