To make the batter, start by adding the sugar and lemon zest to a bowl. Use your hands to rub the lemon zest into the sugar to release the zest's oils.
Next, add the room-temperature vegan butter to the bowl. Use an electric mixer or standing mixer to cream the butter, sugar, and zest together until fluffy (about 2 minutes).
Then, add in the remaining wet ingredients including the plant-based milk, lemon juice, applesauce, and vanilla bean paste/extract. Mix together for another minute. Please note: The batter will be separated and lumpy at this point, but that's okay! It will all come together once the dry ingredients are added.
Add the dry ingredients to the bowl starting with the all-purpose flour and then pouring the baking powder, baking soda, and salt on top.
Use the electric standing mixer to roughly mix everything together for 30 seconds-1 minute. Then, switch to a spatula and continue to fold the dry ingredients into the batter until no streaks of flour remain. It's VERY important to switch to a spatula here or you risk overmixing the batter and forming too much gluten.