You are not the first person to have status with one airline and want miles on another. Don't worry. Your status still counts.

Show your AA Platinum ID card and you'll get lounge access. The agents don't care what program you'll get miles with, only that you have a oneWorld flight that day and a valid reason to be let in. Ditto for check-in, priority security lines if an airport has them, and most other things.

Operational upgrades are not likely to happen, since those usually depend on what the gate agents' computer knows about you and that will be your non-elite status with LAN, but you can console yourself that they're rare anyhow. However, you can casually show your AA card as you ask "Do you do early boarding for AA frequent flyers?" or something like that to make sure the gate agents know.