American and United low fares to London from LAX return in mid-September for all dates into March 2018, except Dec 5-Jan 7 when fares are mostly in mid-$500s.
Ticket prices have regularly been around $550 round trip for most of 2017 so far with all three alliances.
Loyalty Traveler – LAX to London 5 airlines $505-$557 nonstop Jan-May (Dec 21, 2016).
United Airlines ticket for Air Canada and Swiss flights
LAX – Vancouver YVR – London LHR – Zurich ZRH – LAX
$486.86 round trip Sat Nov 18 – Sun Nov 26 (Thanksgiving week).
British Airways nonstop LAX – London LHR – LAX