While rereading the first book Game of Thrones I noticed how Neds describes how he remembers when Lyanna died, the smell of blood and flowers he claims (hinting of the blood from birth). One interesting thing I noticed was that Ned claimed Lyanna made Ned promise her that she would be buried in the crypts. Normally the crypts are ONLY reserved for the head of house Stark, and there has been no women buried there previously.
The TV show makes no reference to this, and in fact the “promise” Ned kept seems to entirely be the protection of Jon Snow. I’ve seen some videos trying to analyze the crypts and I’ remember the reasoning giving to Lyanna being buried there to simply be due to Ned being a sentimental man who had a soft spot. But the books explicitly claim Lyanna made Ned promise her he would bury her in the crypts of Winterfell.
Another interesting part of that scene was how Ned and Robert had the conversation on how he would become the hand of the king. Ned then felt that the eyes of the statues were following him and his ancestors had disagreed with this move. Catelyn Stark also had the sensation that the Weirwood trees were following her through the eyes of the marked face, thinking their long thoughts she said. We now know that Catelyn was right in feeling that the trees were sentient and seeing her, this may be an indication that Ned is also correct and the Stark ancestors are somehow alive as ghosts of some kind. Rhaegar is said to have married and sired with Lyanna in order to fulfill a prophecy, and believed to have been well read on these mysteries. Perhaps he knew something about the crypts and told Lyanna, and thus she was buried in the crypts?
In the TV series we see Lyanna abscessed over not wanting to die. Perhaps she was attempting to live on somehow by being buried in the crypts that may retain some magical element?