Heat the oven to 350°F. Line a 13 x 9 inch baking pan with parchment paper or grease with baking spray.

In a medium bowl, combine the flour, baking powder, baking soda, and salt. Whisk to combine and set aside.

Add the sugar and lemon zest to a large mixing bowl. Use your hands to rub the zest into the sugar. This will release the oils in the lemon zest and bring out the lemon flavor. Toss in the softened butter and use an electric mixer to beat on high speed until light and creamy. Scrape down the sides of the bowl.

Add the eggs, one at a time. Beat well and scrape down the bowl between additions. Blend in the mashed banana, vegetable oil, and vanilla extract.

Beat in half of the flour mixture. Mix in the buttermilk. Use a wide rubber spatula to fold in the rest of the flour.

Pour the batter into the baking pan and bake for 36 to 45 minutes or until a toothpick inserted into the center of the cake comes out clean. Cool the cake in the pan for 10 minutes before inverting it onto a cooling rack to cool completely.