A certain level of colour variation is part of the natural beauty of lime wash paints. Looking at the photo below the variation is, in most parts, at an acceptable level.
Adding more coats may even it out, but sometimes we have found it also made it more pronounced. It really depends to al large degree on the initial preparation of the walls that causes some colour variation.
Our Recommendation:
If you add another layer that is fine as long as it is painted very quickly. Sometimes the white spots can appear if the brush is moved too many times across the same spot with too little paint. It is best to work with fast and loose strokes and it does not matter if you miss small bits as you have already a good colour base.