Last night he had dreamed of Sam drowning, of Ygritte dying with his arrow in her (it had not been his arrow, but in his dreams it always was), of Gilly weeping tears of blood. DwD Jon III

She wore a garland of pale blue roses, and her eyes wept blood. Eddard XIII

We know in general the reason for why we are seeing Gilly weep tears of blood. He child was taken from her. Might the same be true for Lyanna? Have you had the chance to read through either of these threads? www.thelasthearth.com/thread/356/jon-starfall or thelasthearth.com/thread/220/asos-chapter-80-sansa-vii

They might seem completely unrelated but some of the echo/background work exists in each of them. I know that there are things in that Sansa chapter that made me consider Starkcest and even add Rickard Stark to the list of suspects. Especially if you choose to look at the Harrenhall crowning as more of a subtle threat by Rhaegar than an honor. The thing is looking at Lyanna's baby as possibly being taken away or swapped out opens up so many more possibilities with regards to the timeline. You can add in an earlier birth and consider people like Robert, Ned and Rickard that way.