Preheat oven to 425°F. Place muffin liners in a 12 count muffin tin or spray with non stick spray. Set aside.
In a medium bowl, whisk together flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, whisk together olive oil, coconut oil, sugar, yogurt, and lemon juice and zest until fully combined. Add egg and vanilla, and mix thoroughly.
Add dry ingredients to wet ingredients in two additions, stirring until just combined. Fold in poppy seeds.
Pour batter into prepared muffin tin, filling 3/4 of the way full. Bake for 5 minutes at 425°F then reduce heat to 350°F and bake for another 8 to 10 minutes, until muffins are golden on top and a toothpick inserted in the center comes out clean.
Allow to cool in pan for ten minutes then transfer to cooling rack to cool completely.
To making the icing, whisk together the lemon juice and powdered sugar. Fill plastic bag or piping bag with the icing and cut off a very small portion of the tip with scissors. Pipe the icing on top of the muffins in a back and forth design. Allow to set for approximately 5minutes.
Keep in an air tight container for up to 5 days.