Jon saw lady in his dreams because in theon dreams greywind and Robb were together to imply that their death occurred simentaenously but the direwolf Jon saw was sad and lonely and in crypts where lady is buried. But why he saw ygritte there?
Hi there!
Ygritte comes up at the strangest moments and for different reasons. Sometimes her name is not mentioned, but her trademark insult to Jon: You know nothing, Jon Snow. Jon knowing nothing is connected to several things but the most obvious thing Jon doesn’t know is his parentage: For that reason it is interesting, that Jon dreams about the Old Starks telling him that he is no Stark and about Ygritte.
There is another reason though, I would say. On a conscious level, Ygritte reminds Jon of Arya. On a subconscious level, some of Ygritte’s traits Jon is attracted to are connected to Sansa, without Jon ever drawing an explicit comparison.
Sometimes she sang in a low husky voice that stirred him. And sometimes by the cookfire when she sat hugging her knees with the flames waking echoes in her red hair, and looked at him, just smiling . . . well, that stirred some things as well. (ASOS, Jon II)
Sansa sings and Sansa has red hair and both these traits stir something in Jon.
The firelight playing in the hair is something that is explicitly said about Sansa:
I often sent away her maid so I could brush her hair myself. She had auburn hair, lighter than mine, and so thick and soft . . . the red in it would catch the light of the torches and shine like copper. (ACOK, Catelyn VII)
The wording is completely different, but the image is the same.
And Sansa does not only sing, she sing sweetly:
Her sister had known all the songs, and she could even play a little, and sing so sweetly. All I could ever do was shout the words. (ASOS, Arya IV)
So both, the singing and the hair colour are definitely not the traits Ygritte shares with Arya, but with Sansa. And Jon’s reaction is “it stirred some things”.
Please remember that that does not mean that Jon has sexual feelings about Sansa at the moment: It just means that he is attracted to singing and red hair in the firelight.
Anyway, Ygritte turns up again and again, and sometimes she is a reminder of Sansa: When Jon is offered Winterfell, he thinks that he might be tempted to take Stannis’ offer if Ygritte was alive. He thinks Melisandre is Ygritte at one point (ADWD, Jon VI).
I think the most significant thing is this though, shortly before Jon dies:
He thought of Robb, with snowflakes melting in his hair. Kill the boy and let the man be born. He thought of Bran, clambering up a tower wall, agile as a monkey. Of Rickon's breathless laughter. Of Sansa, brushing out Lady's coat and singing to herself. You know nothing, Jon Snow. He thought of Arya, her hair as tangled as a bird's nest. (ADWD, Jon XIII)
Jon thinks about the Starks and there is Ygritte’s mantra right between the two sisters. And Sansa is there with Lady (non of the other Starks is in Jon’s memory with their direwolf). And Sansa is not only with Lady, but Jon remembers her singing, one of the things he really liked about Ygritte (cf. my meta on singing in Jon’s arc on that) and then there is Arya. And for her there is also a connection with Ygritte: the tangled hair, that made Jon remember his little sister when he observed Ygritte (and not in a positive way: he contemplated asking Ygritte if she knew how to brush: Lucky it might be, and red it certainly was, but Ygritte's hair was such a tangle that Jon was tempted to ask her if she only brushed it at the changing of the seasons, ASOS, Jon II). So, there is the subconcious and the conscious almost right beside each other if it were not for Ygritte’s mantra.
To me this is a reminder of the dream in the crypts, the Starks are there, Lady is there and Jon does not know anything, not his parentage nor his heart probably. Because he does not yet know what Sansa’s singing will do to him. “What do you know of my heart, priestess?” I am tempted to ask: “What do you know about your own heart, Jon?” Nothing is the answer, as for now.
So, I would say, there is a reason why Ygritte is mentioned in Jon’s crypt dream and it is more than just his bad conscience about her death. I think Jon’s thoughts before his death are very strong Jonsa foreshadowing but J0nryas see that very very differently. lol.
Thanks for the ask!