United Airlines has $490 round trip tickets from Los Angeles LAX to London LHR with nonstop flights outbound and one-stop Swiss Airlines flights inbound. The price rises to $575 for nonstop both directions.
Departure dates run from October 2 to March 20 with December holiday dates excluded. Most dates are available at $490 round trip.
Interestingly, these $490 United/Star Alliance fares do not show up in Momondo.com searches I made for same dates with lowest fares at $553 for Air New Zealand nonstop flights.
United Airlines Los Angeles LAX – London LHR – Zurich ZRH – LAX