Preheat the oven to 350°F (175°C).
Pour the melted butter into the bottom of a 9-inch round cake pan and spread evenly.
Sprinkle 3/4 cup granulated sugar evenly over the melted butter.
Arrange the lemon slices in a single layer over the sugar and butter mixture.
In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large bowl, beat the softened butter and 1 cup granulated sugar together until light and fluffy, about 3 minutes.
Add the eggs one at a time, beating well after each addition.
Mix in the vanilla extract, lemon juice, and lemon zest until combined.
Alternately add the flour mixture and milk to the butter mixture, beginning and ending with the flour mixture. Mix until just combined.
Pour the batter evenly over the arranged lemon slices in the cake pan and smooth the top.
Bake for 40 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Remove the cake from the oven and let it cool in the pan for 10 minutes.
Run a knife around the edges of the pan to loosen the cake.
Place a serving plate upside down over the cake pan and carefully invert the cake onto the plate.
Lift the pan off gently. If any lemon slices stick to the pan, place them back on the cake.
Allow the cake to cool slightly before serving.