When you click on the document link here;
https://identifyus.org/en/medias/download/17149 and then after opening and viewing go to "file" and click on that, at the bottom where there is a list of attached documents to this PDF file, it says " death_certificate_issued_3-18-1967[1]" and other files, but that one date struck me as a clue to the date of death for the real LEK. Searching ancestry.com for LEK's first name and that date of death or March 1967, there is someone (actually several someones) but not with "K" as a last name!
Searching for missing persons with a date of birth in 1969, here are the females I came up with;
http://www.charleyproject.org/cases/c/calico_tara.html < went missing 1988 and could've been forced into




or something degrading, wouldn't want that coming up or scared the kidnappers would find her. And the other similar looking MP is
http://www.nampn.org/cases/berens_lori.html in which another sleuther has already mentioned on this thread!
So, LEK must've obtained the SS# with a birth certificate and then added a few years to the actual birthdate of the real "L" that is probably closer to LEK's real year of birth!
Whew! Time consuming and mind blowing, for sure!
ETA: When a person dies and is sent to the funeral home, the first thing the coordinator does is issues a death certificate based on the SS# so that creditors, etc. can be given a copy, actually one must be issued before burial, so that's when it was probably discovered about the assumed identity!