Suggest you go to ual.com and download a timetable.
UA has a very large international route network. In addition there are plenty of domestic 777 flights. And yes UA does have several international flights from LAX. LHR, NRT, MEX, YVR, SAL, UA / MGGT), Guatemala">GUA, SYD of the top of my head.
From the desert to the sea, to all of Southern California
TriJetFan1 -- as your'e looking at the timetable there is a column which shows how many stops the plane makes en route from LAX to the ultimate destiation. The ones with a "0" would be the non-stops. Hope that helps!