American Airlines/Oneworld Alliance have $490 round trip tickets for LAX to Barcelona. Itineraries I checked showed Iberia’s Level flight in one direction for this fare. The price is $500 for all American flights. These fares are April 2018 travel departures.
British Airways AARP $65 discount rate drops price to $435.30 round trip for AA flights.
United Airlines/Star Alliance have similar fares at $500 round trip.
Los Angeles LAX – New York JFK – Barcelona BCN – JFK – LAX
United Airlines LAX – Newark EWR – Barcelona BCN – EWR – LAX