You are somewhat correct - and when / if Mexicana becomes a oneworld partner, that will apply, as then it would be both operated and marketed by a oneworld airline. Curretnly, it is not, so the OP would be eligible to use the TBIT MX lounge (assuming there is one) or the AC if in possession of a valid card for using the AC (AC, eligible QF, etc.)

"oneworld benefits are available to qualifying passengers and eligible guests on scheduled flights that are both operated and marketed by a oneworld member airline. Eligible passengers have access to either the Admirals Club lounge or Flagship Lounge facility (where available) on the day of their departure."

OTOH, the OP would have a bit of a challenge using the LAX AC and running over to deal with the queues at TBIT to process for the MX flight - perhaps MX has a lounge in TBIT s/he can access.

(In Mexico City, the MX lounge has a good-sized fitness facility adjacent, and not much else to recommend it - I prefer the somewhat old-fashioned Admirals Club in MEX to the international Mexicana lounge, and they are close to each other.)

MX sometimes does provide courtesy upgrades, to its own elite FF members and sometimes to AA elite status members, but it should not be counted on. Hint: Most of us Latins are more relationship-oriented, so some initial courtesies and friendliness make it more likely an inquiry might result in an op up. As for the rest of us, well...