Short answer is no unless you want to route via LHR.
I presume that you want to fly direct? If so you could use Avios to fly JL to TYO if you can find seats but not the companion voucher.
Your chances of finding F space via LHR is minimal as LHR-HND only has a total of 8 F seats available for sale each day in October. That's if you can find F space from LAX.