Preheat oven to 350°F. Grease and line a loaf pan with parchment paper.

In a large bowl, whisk sugar and eggs until light and frothy, about 1 minute.

Add milk, butter, lemon juice, lemon zest, and vanilla to the egg mixture and whisk until smooth.

Add the gluten-free flour, baking powder, and salt. Gradually stir in the dry ingredients until just combined. Do not overmix.

Pour the batter into the prepared loaf pan and smooth the top.

Bake for 45–50 minutes, or until a toothpick inserted in the center comes out clean.

Let the loaf cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.

For the icing, whisk powdered sugar, lemon juice, and salt until smooth. Drizzle over the cooled loaf.