Preheat the oven to 350°F (175°C).
Cream the softened butter and granulated sugar together until light and fluffy, about 3 to 4 minutes.
Add the eggs one at a time, mixing well after each addition.
Mix in the lemon zest and fresh lemon juice until fully incorporated.
In a separate bowl, sift together the flour, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the wet mixture, alternating with milk, mixing until just combined.
Fold in the poppy seeds gently to evenly distribute them in the batter.
Pour the batter into the greased baking pan and spread evenly.
Bake for 25 to 30 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes, then transfer to a cooling rack before serving.