> that storyline never went anywhere

I mean, that has more to do with GRRM not writing anything for the past decade.

I think there will probably be a couple big roles for LSH in the books. First, she'll be a model for how fucked up the process of resurrection can leave a person. When Jon is resurrected, I think there will be a lot more uncertainty about his temperament, and whether it's even still Jon in there.

Second, I think at some point she'll meet Arya. They both have similar goals in exacting revenge against those who wronged House Stark, in particular those involved with the Red Wedding. I think this will bring them together, and seeing her mother as a fucked up revenant murdering her way through the Riverlands will be what finally steers Arya away from revenge. It would be a more compelling resolution to that character arc than the Hound looking at her and telling her "actually, don't kill Cersei" at the eleventh hour.