Lyanna survives the child birth but still makes Ned promise not to reveal her son’s father to Robert. Instead Ned’s bride is welcomed at Winterfell by a weak but recovering Lyanna and her “nephew” Jon Snow.
With the war over everyone expects Robert, The Hero, to marry Lyanna, His Lady Love, and he pushes for it, ignoring those who point out that Lyanna would be “tarnished” after her time with Rhaegar.
Lyanna would also refuse…at first, but with the entire country knowing that this war was partially for her and needing to keep Jon safe she ultimately agrees and marries Robert with the condition that Ned bring her beloved nephew to visit often.