Umm.. The OW lounge access policy for Asia is pretty clear

if departing on an OW carrier in First or Business , he is entitled to lounge access
Since departing on a OW carrier in Economy, no OW lounge access so expect JL to decline admission

AA has their own additional rules of admission which would allow access to those with a same day international flight in a premium cabin, so the AA lounge if conveniant , will likely allow access

Dave