Air Tahiti Nui in April and May 2015 is operating 1 round-trip Los Angeles – Lourdes service, with the flight time of 11hrs 50mins from LAX, 13hrs 10mins from LDE. This is a charter flight therefore it is not available for bookings to general public.
TN721 LAX1530 – 1210+1LDE 343 28APR15
TN732 LDE0950 – 1400LAX 343 06MAY15
Flight schedule is listed in Amadeus timetable listing as well as the OAG.