Oneworld's own press release on the new LAX lounge states that:
"The new Business Lounge is available to passengers booked in First or Business Class on oneworld airlines departing from the terminal, or customers holding Emerald or Sapphire status in any oneworld member airline's frequent flyer programme booked in any cabin on a oneworld member airline flight from the terminal."
So they can deny you entry if your OW flight leaves from a different terminal but not if you're on a domestic OW flight departing from that terminal....
url]https://www.oneworld.com/news-information/oneworldnews/-/asset_publisher/QtTQ7EuCzxhd/content/new-los-angeles-lounge/maximized[/url]