Star Alliance member airline Air China has Los Angeles LAX to Osaka, Japan KIX for as low as $593 round trip for departures beginning August 24 and into September. This is a hard fare to search since it doe not show on Google Flights. I used ITA Matrix Airfare Search to find low fare departure dates from LAX.
ITA Matrix Airfare Search shows Air China at $604 round trip beginning August 24, 2016 for several dates in August and September.
Once I had low fare dates I could search Google Flights filtered for Air China for direct links to low fare dates.
Air China Los Angeles – Beijing PEL – Osaka, Japan KIX
$592.71 Wed Aug 24 – Wed Aug 31 (overnight in Beijing, depart Sep 1) arrive LAX Sep 1
This ticket books in Air China economy class L. Earn 25% flight miles with United Mileage Plus or even more miles with other Star Alliance frequent flyer programs, like 100% flight miles with Aegean.