Tough issue.
Could you not have used online check-in forLAN.
http://www.lan.com/en_un/reservas/de...s_chequeo.html
Did you specifically ask/ did attendant say at MAN or LHR whether you had been checked in for the ongoing flight?
I would find it weird that luggage would be tagged thru without you being checked in
FYI the published -- AA-LA MCT for JFK I/I is 1hr15