Just near the Church of the Nativity is the Milk Grotto which is a popular veneration site. The Milk Grotto is said to be the location where Mary, Joseph and the Infant Jesus temporarily sought refuge during the incident of the Slaughter of the Innocents.
It is also in the Milk Grotto where Mary was able to nurse the infant Christ before they traveled to Egypt. It is said that a drop of milk from Mary dropped to the ground, which turned the color of the rock floor, white. The soft white rock of the grotto is popularly thought of as having healing powers as well as health benefits for lactating mothers.
Thank you! I just wrote in my previous post that I never saw Mary breast feeding in Orthodox iconography, but you may just have proven me wrong, although the last painting in your post doesn’t look Byzantine.