Preheat oven to 350°F and line a mini loaf pan with parchment paper, leaving a slight overhang for easy removal.
In a large bowl, add the granulated sugar and lemon zest. Rub them together with your fingers until the mixture becomes fragrant and slightly damp, this helps release the natural oils from the zest.
Add the melted dairy-free butter, applesauce, vanilla extract, lemon juice, dairy-free yogurt, and almond milk. Whisk until the mixture is smooth and fully combined.
Add the flour and baking powder. Gently mix using a spatula until just combined and no dry streaks remain. Do not overmix. The batter will be thick but smooth.
Pour the batter into the prepared loaf pan and spread evenly to the edges. Tap the pan lightly on the counter to remove any air bubbles.
Bake for about 20 minutes, or until the top is lightly golden and a toothpick inserted in the center comes out clean or with a few moist crumbs.
Allow the loaf to cool in the pan for 10–15 minutes, then carefully lift out and transfer to a wire rack to cool completely before glazing.