Preheat oven to 350F.
Spray an 8-9" loaf pan with baking spray and set it aside.
In a large bowl, whisk yogurt, olive oil, eggs, and vanilla until smooth. Add sugar and salt and whisk for 2 minutes.
Measure out the flour and stir in the baking soda and baking powder. Add these dry ingredients a third at a time, to the wet mixture, whisking away any lumps.
Add the lemon zest, fresh lemon juice, and poppy seeds, whisk again, until combined.
Pour the batter into the greased loaf pan. Bake for 55-60 minutes, or until an inserted toothpick comes out clean and the cake is puffed and golden.
Let the cake cool for 15 minutes. Slide a knife down the sides to loosen the cake from the pan. Place on a cooling rack.
Whisk together the icing and drizzle it over the cake once it's completely cooled.