Of course Lyanna would understand if Jon wanted nothing to do with her. She had single handedly managed to get most of her family killed. What kind of kid wanted a mother like that? She nodded her head and diverted her eyes when Jon said he couldn't promise anything.
And then he said he would promise to try and that's all Lyanna needed to hear. Her face lit up and she reached out to pull Jon into a hug as her eyes misted up.