Preheat your oven to 350°F (176°C) and lightly grease a 9" x 5" loaf pan with butter or cooking spray.
In a large mixing bowl, whisk together the flour, salt, baking powder, baking soda, and set aside. (If fermenting the batter overnight, omit the baking soda and baking powder and add it just before baking.)
Melt the butter in a bowl and add the sugar. Use a spatula to cream them together until smooth. Add the egg, sourdough discard, lemon juice, lemon zest, and applesauce, and mix until well combined. Pour the wet ingredients into the dry ingredients bowl and stir until just combined. Pour the batter into the loaf pan. (If fermenting overnight, cover the bowl and place in the fridge.)
Bake on the center rack for 55-60 minutes or until a toothpick inserted in the center comes out clean. Allow to cool for 15 minutes before transferring the cake to a wire rack.
Mix the powdered sugar and lemon juice in a small bowl and drizzle over the cake.