Aunt Diane

In the film, they mention she died in-between timelines. You can assume she raised Libby for a while.

In the book, it's a bit different: she adopts Libby, gains a lot of weight, and I think she eventually kicks Libby out because Libby kills her dog (it's ambiguous whether or not it was an accident, but in any case Libby expresses little remorse--this is mentioned in the movie, indirectly, when Libby says she's "killed things").

I might be wrong about Libby getting kicked out, though; it's been almost a year since I read the book. In any case, Diane is alive in the book, though understandably on bad terms with Libby. Libby kind-of-sort-of-but-not-really makes up with her at the end of the book, but the bulk of her scenes in the book happen in the eighties timeline, just like in the movie.