It is a hand written paper ticket? If yes and if you arrive at LAX sixty minutes prior to the flight, you will most probably miss the flight.

IME, agents at LAX don't like dealing with RTW re-issues even when all they have to do is print the ticket and collect the change fee. It becomes a lot worse when they have to hand write a paper ticket.

Call the RTW desk to make all the necessary routing changes, re-calculate the taxes, etc, before you arrive at the airport. This will help save time and help reduce the number of problems you (might) run into.