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The AA website and access policy is a little contradictory, but this is a Qantas Lounge ...
• Any one on an AA or other OW Domestic flight, originating their journey in LAX regardless of status or cabin to be flown, does NOT have access to the Qantas First or Business Lounges.
That excerpt contravenes Qantas' own published rules:
Lounge Locations | North America | Los Angeles International Airport Tom Bradley Terminal | International Business
Eligible oneworld Status
Emerald
Next onward flight that day must be on a oneworld operated and marketed flight.#
One guest allowed and must be travelling on a oneworld operated and marketed flight.#
Sapphire
Next onward flight that day must be on a oneworld operated and marketed flight.#
One guest allowed and must be travelling on a oneworld operated and marketed flight.#
and
Eligible Qantas Members
Platinum One Frequent Flyer
Next onward flight must be on a Qantas, Jetstar Airlines+ or oneworld operated and marketed flight.#
One guest allowed and must be travelling with the member on the same flight.
Platinum Frequent Flyer
Next onward flight must be on a Qantas, Jetstar Airlines+ or oneworld operated and marketed flight.#
One guest allowed and must be travelling with the member on the same flight.
Gold Frequent Flyer
Next onward flight that day must be on a Qantas, Jetstar Airlines+ or oneworld operated and marketed flight.#
One guest allowed and must be travelling with the member on the same flight.
Qantas Club Member
Next onward flight that day must be a Qantas, or Jetstar Airlines+ flight number.
One guest allowed and must be travelling with the member on the same flight.[/TD]
+ Jetstar refers to Jetstar (JQ), Jetstar Asia (3K) and Valuair (VF).
# A oneworld marketed flight refers to a flight with a oneworld flight number, eg QF1 or AA222. A oneworld operated flight refers to the actual aircraft or 'metal' on which you fly, eg Finnair aircraft.
Note: Complimentary invitations cannot be used in the Los Angeles oneworld lounge.
The only thing not referred to on the Qantas page there is the oneworld caveat for AAdvantage Elites:
American Airlines AAdvantage® members and US Airways Dividend Miles members, regardless of their tier status or class of travel, are not eligible for lounge access when travelling solely on North American flights within or between the U.S., Canada, Mexico (except Mexico City), the Bahamas, Bermuda and the Caribbean.