Preheat the oven to 400° and line a muffin tin with oil or paper cups.
In a large bowl, mix together the oil and sugar and mix until the sugar starts to break down. Add in the eggs, and mix well. Add the lemon zest, lemon juice, yogurt and milk, and mix until well combined.
In a separate bowl, mix together the flour, baking soda, baking powder, salt and poppy seeds.
Add the dry ingredients to the wet ingredienst and mix until just combined. The batter will be thick.
Scoop out evenly into a 12 cup muffin tin. Bake for 10-15 minutes or until a toothpick comes out clean. Let muffins cool completely before glazing.
To make the glaze, whisk the lemon juice and icing sugar together until smooth. If the glaze seems too runny, you can add a bit more icing sugar. Drizzle on top of the muffins.
Notes
Use an all purpose gluten free flour to make these gluten free. Make sure your poppy seeds are fresh and haven't gone rancid.