I am flying in to LAX on American Airlines and have a 60 min layover before I fly out with American Airlines (same ticket).
Will this be enough time?
Talking based out of experience.
American Airlines operates from Terminal-4 (http://www.lawa.org/LAXAirlines.aspx). They also operate from Terminal 6, gates 60-63 as mentioned on the LAX web site.
1) If your connecting AA flight is from the same terminal as that of your arrival, 60 minutes is good enough.
2) If your connecting AA flight is from another terminal i.e. either T4 to T6 or T6 to T4, you should still be good as the commute between T4 and T6 is small and the airport provides shuttle services too.
I have done international transits with connections of 60-75 minutes. However, immigration and security for international travel might take much longer and hence I would recommend a longer transit time.
Hope this helps.
As it is a single ticket, it should be OK. The airlines know how long of a connection is necessary at each of their hubs and create itineraries that meet those anticipated connection needs.
That said however, you don't have any leeway time to stop and grab food or drink. And if your incoming flight is delayed, you could be doing the LAX dash.
My experience of Lax is that of an efficient airport. Within the same terminal you don't have anything to worry about and most likely that would be the case. Even across terminals since you will already have your boarding pass and your luggage will already be checked in, this time should be sufficient.
Once you are in a TSA queue which is blind to the time when your flight closes, it all depends on your luck as well as on the ability of other passengers to follow simple instructions like not having liquids in their bags. I have missed tight connections like this a few times but airline always accommodates on the next flight so it has never been a major inconvenience.