I've also tried to see if the "60 Minutes" story on identity theft from the 1980's is anyplace online, but I have not yet found it. If it was broadcast prior to 1988, it could certainly have helped this woman as well.
I remember watching that episode of 60 Minutes at my parents' house before I started college. (I attended college 1976-1980.) Which puts it in the early 70s, & even if my memory is failing, no later than 1978 when I moved out.
Maybe it was aired too early for LEK to have used for her own identity theft, but if I thought of it a year when I first became serious about this mystery, I'd be surprised if LEK hadn't thought of it when she decided to reinvent herself. And other posters have mentioned similar ways that she could have learned of these tricks.
As for the fact that she managed to find the right identity to steal, which seems to be too unusual to be just happenstance, all it takes is unusually good luck on her part: somehow learn of this unfortunate dead girl, notice she died in a state different from the one she was born in, & decide to exploit the knowledge. If finding such a combination is a one-in-a-million chance, that probability still means at least one person found that combination. (And AFAIK, there has been only one other case like this -- of a successful identity theft uncovered only thru the perpetrator's death.)