At this site, the OP can see the nonstop destinations served from LAX by all airlines, including DL (SkyTeam); AA and AS (oneworld); and UA (Star Alliance):
https://en.m.wikipedia.org/wiki/Los_...tional_Airport
If flying AA/AS would suit the OP, I would join the Iberia FFP and the Royal Air Maroc FFP, and see if either would offer a status match now to at least oneworld Sapphire (mid-tier) status. That would provide lounge access and some decent benefits on AA/AS. The likelihood of a status match would, I think, be greatest when the OP can show a lot of recent flight activity.