Preheat oven to 350°F. Grease two 8" or 9" cake pans or one 9"x13" dish for a sheet cake. Line the bottom of the cake pans with parchment paper for easiest removal. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream butter, sugar and vanilla on high for one minute until light and fluffy. Scraping the sides as needed.
Add eggs one at a time, mixing until fully incorporated after each addition.
In a medium bowl, mix flour, salt and baking powder.
In a small bowl, combine milk, lemon juice and lemon zest.
Alternate milk mixture and flour mixture into the butter mixture in 3 additions, ending with flour. This ensures all of the liquid is thoroughly incorporated into the batter and prevents the mixture from "splitting".
Scrape the sides of the bowl and mix until fully combined, but careful not to over mix.
Pour the batter into the pans, dividing evenly if using 2 cake pans. Bake on center rack for 25-30 minutes, until center springs back when lightly touched or a toothpick comes out clean.
Allow to cool in pans for 5 minutes, then remove and allow to fully cool on cooling racks.