I would expect AS to issues the JAL boarding pass for the JL flight. They are partners for US connections. JL will probably reprint the boarding pass in LAX No need to leave the lounge for that

If AS does not print a boarding pass, the lounge will help with that. Just make sure he has a printed version of the itinerary. He will not be denied at the lounge if he has that.

If he has luggage, I don't know if AS can or will check it through to CX. If not, ask at the LAX lounge if JAL can reroute it. If not he will have to reclaim and recheck in Narita.

If he does not have a CX boarding pass, a printed itinerary is enough for transit security in Narita. (provided he does not need to reclaim luggage)