American Airlines has an unusual fare for LAX to New York LGA or vice versa at $210 round trip from September through March 2017. This fare is widely available most dates each month. What is unusual about this fare in 2016 is the lowest one way price is $148 to $152 and this fare is not priced as two one-way fares. Anyway, great deal for LAX to NYC with loads of availability from September through end of schedule. No other airlines are currently under $300 round trip for LAX-NYC.
Google Flights shows $210 fare availability nearly every date in September-October 2016.
American Airlines Los Angeles LAX – Dallas DFW – New York LGA
$209.20 Saturday September 10 – Saturday September 17