Preheat the oven to 350°F. Spray a 9x13 baking dish with baking spray, set aside.
In a medium-sized bowl, mix together the flour, baking powder, and salt, set aside.
In the body of a stand mixer with the paddle attachment, cream together the butter and the sugar and until light and fluffy, 2 minutes.
Scrape down the sides. Add the eggs in one at a time, allowing them to fully combine into the mixture.
Scrape down the sides and add the flour mixture. Gently stir it in until just combined.
Add the milk, lemon juice, lemon zest, and vanilla, stir in until combined, scrape down the sides.
Last, add the poppyseeds and stir them in until evenly distributed, do not over mix.
Add the cake batter to the baking dish and bake for 35-42 minutes, until a toothpick inserted into the center comes out clean. A few crumbs left on the toothpick are okay, but any wet batter and it needs to bake longer.
Place the dish on a wire rack to cool completely.
While the cake cools, make the frosting by placing the butter into a large bowl with an electric hand mixer. Mix until smooth, 1 minute. Add the powdered sugar a little at a time until fully incorporated. Add the lemon juice, zest, and vanilla, mix until combined. Turn the mixer on medium and whip the frosting until light and fluffy, 3 minutes.
Once the cake is cooled, frost with lemon buttercream. Slice and serve.