Preheat oven to 350 degrees Fahrenheit.
In a bowl, combine flour, baking powder, baking soda, lemon zest, and salt. Set aside.
With a hand mixer, cream the butter until fluffy. Add the sugar and cream for 4 minutes or until pale and fluffy.
Add eggs one at a time, mixing after each addition until combined. Add vanilla and lemon juice. Mix until incorporated.
Add the dry ingredients and buttermilk alternating between the two, ending with the dry ingredients.
Fold in the poppy seeds with a spatula.
Grease a Bundt cake and fill with cake batter. Bake for 35-40 minutes until golden brown or until toothpick inserted near the center comes out clean.
Mix together the 3 tbsp powdered sugar and 1/4 cup lemon juice. Brush on poppy seed cake while still warm but not hot.
For the glaze: In a medium bowl, combine powdered sugar, lemon juice and milk until it reaches a thick but spreadable consistency. If icing is clumpy, strain through a sieve. Pour over cooled bundt cake and serve.