Place the rack in the center of the oven. Preheat the oven to 325°F (163 °C) with a rack in the center of the oven. Line a 9”x13” pan with a piece of parchment paper.
In a medium mixing bowl, stir together the flour, salt, and baking powder. Set aside.
In a large mixing bowl with an electric hand mixer or a stand mixer with a whisk attachment, beat the eggs, sugar, vanilla extract, and lemon extract at medium-high speed for about 2 minutes until it's thickened and a light gold color. Should your stand mixer not have a whisk attachment, then beat the mixture for 5 minutes using the paddle attachment.
Beat in the dry ingredients on low speed just until combined. Use a silicon spatula to scrape the bottom and sides of the bowl and mix briefly to incorporate.
In a small saucepan, heat the milk and lemon zest over medium heat. You shouldn't let it boil. When you see tiny bubbles start to appear around the edge of the saucepan, it's ready. The temperature will be 180-185 °F (82-85 °C). Remove the pan from the heat and stir in the butter and oil until the butter has melted.
Slowly stir the milk mixture into the batter at low speed and mix until totally combined.
Bake the cake for 33-40 minutes or until the edges are pulling away from the sides of the pan, a toothpick inserted into the center comes out clean, and the top feels set. A digital thermometer inserted into the center of the cakes should read 205 °F.
Remove from the oven and place on a wire rack to cool completely, about 2 hours (if decorating the cake right away - read the section below). You can bake, cool and tightly cover the cake pan with plastic wrap. The unfrosted cake can sit at room temp for 2 days, or you can refrigerate it for up to 3 days. You can also freeze the unfrosted cake for up to 3 months. But I don’t recommend freezing the frosting.