I was able to find seats on American departing Atlanta ATL on Saturday, November 3, returning from Los Angeles LAX on Tuesday, November 6.
You'll find other scattered dates on American for travel through mid-February, excluding peak holiday travel. $206 roundtrip travel on Southwest is only available on a few dates in early December, but $103 one-way flights from Atlanta to L.A. can be found starting in September.
American Airlines is Basic Economy for this price, but this will include a normal carry-on bag plus one personal item starting in September. If you would like to choose a specific seat or don't like the other restrictions of Basic Economy, upgrade to the Main Cabin Economy fare for $36 more.
Southwest includes two free checked bags and has no change fees. Lower fares may be available on Spirit or Frontier, but if you travel with more than just a small personal item, the bag fees will counteract any savings.
Need a place to stay in L.A.? Check out what's available for the listed dates on Hotelwatchdog.