As Air Tahiti Nui, your international flight, is not part of the oneworld alliance you will not have access to a lounge in ORD. On your outbound from LAX and your return from PPT you will have access to the lounges that Air Tahiti uses for business class customers as your flight will be an ATN prime flight number. Returning from LAX you will not have access to a lounge there.

Do be aware that if you want to make full use of your connection time for the Star Alliance Lounge on the outbound flight from LAX you will need to exit security and go to the check-in desks to get the lounge admission cards. The departure gate usually isn’t manned until 75-90 mins before departure which would limit the amount of time for the lounge if you wait for the gate agents.