Madrid with Star Alliance
A minor LAX fare war between Oneworld and Star Alliance sees Madrid and some other cities across Spain at $520 and lower for round trip flights with United, Lufthansa, Swiss and partners for travel Feb-early May and resuming in mid-August.
Momondo.com OTA links have fares around $489, possibly even lower.
TravelMerry.com online travel agency ticket
LAX – Newark EWR – Lisbon LIS – Bilbao BIO – Frankfurt FRA – LAX
Frankfurt with Oneworld
Frankfurt is the main destination I see on sale at below average prices with Oneworld. Same Feb-May time frame with Google Flights showing $540, but British Airways AARP discount reduces the Frankfurt fare closer to $441.
British Airways AARP Discount ticket (booking site link)
Los Angeles LAX – Dallas DFW – Frankfurt FRA – DFW – LAX
(Google Flights sows $540 fares for these dates).