United Airlines has a very low $147 round trip fare between Los Angeles LAX and New Orleans MSY for departures from late March through June 15. Low fare available any day of the week, except Thursdays from LAX. The flight from LAX to MSY tends to be a nonstop red-eye.
United Airlines Los Angeles LAX – MSY New Orleans
$146.20 Friday April 8 – Tuesday April 12
LAX-MSY-LAX = 3,342 flight miles. $118.00 base fare for Mileage Plus redeemable miles.