LAX to Barcelona is priced as low as $354 round trip for no frills Level nonstop flights operated by Iberia or about $405 round trip flying United and Star Alliance airlines. Lowest priced flights are for travel in September and October. Ticket prices rise to $500s in November.
Both tickets earn frequent flyer miles with Level earning Avios and Star Alliance airlines earning miles in a variety of programs. I apply Air Canada and United cheap flights to my Aegean Miles+Bonus account where each mile flown is 0.5 Tier Miles. As few as 24,000 Tier Miles earns Star Alliance Gold elite.
Level Airlines Los Angeles LAX – Barcelona BCN – LAX nonstop flights
301.92 EUR ($350.66 USD) Sun Sep 30 – Wed Oct 10
United Airlines Los Angeles LAX – Newark EWR – Barcelona BCN – Washington IAD – LAX nonstop flights
These tickets do not have direct booking links through Google Flights. Tickets priced on Expedia for Star Alliance itineraries I checked.