Yep lime wash is breathable and white so good for lighting :P

Before in the dryer part of the my room you could feel moisture on the walls around 4-5 feet up, now the worst wall (external one) only feels damp at the bottom 1-2 feet but it is improving. I think when there is a couple more coats of lime wash it will spread the moisture out so with some extra ventilation / air circulation I hope it will improve.

By the looks of your pics the walls have the white flakey stuff efflorescense so its probably best to go for a breathable paint.

I am also pondering making a simple air heat exchanger for the vents to help improve the temperature, that will likely be a job for next autumn/winter.