Preheat oven to 350°F (175°C).

Grease and flour an 8x4-inch loaf pan.

In a small bowl, cream softened butter and sugar until light and fluffy.

Add eggs, one at a time, beating well after each addition.

Stir in the unsweetened applesauce, vanilla extract, and grated lemon zest.

In a separate bowl, combine the all-purpose flour, baking powder, and salt.

Gradually add the dry ingredients to the creamed mixture, mixing just until blended.

Transfer the batter to the prepared loaf pan.

Bake for 45-55 minutes, or until golden brown and a toothpick inserted into the center comes out clean.

Cool in the pan for 10 minutes before removing to a wire rack to cool completely.