I have found CO able to interline with even obscure airlines - I'm not certain on Air Tahiti Nui but don't know why there would be an issue. Allow yourself extra time because sometimes the agents are not experts in interlining - patience will go a long way. Double check the bag tags to ensure they are going to the correct airport code. Be certain you have your booking reference for Air Tahiti Nui and then you'll need to present your baggage reference numbers when you check in at Air Tahiti Nui at LAX. Have a great trip!