The issue has since been resolved and operations have returned to normal.
"We appreciate customers' patience, and we encourage our LAX customers to check their flight status on Southwest.com," a spokesperson said in a statement.
In a tweet earlier Friday, the airline said an outage was affecting operations, and the airline was working with the airport to resolve the problem.
A spokesperson said the performance issues were with "systems that support our airport check-in process."
The outage temporarily affected inbound and outbound flights. The airline said there was a similar issue in Austin, Texas. It was unclear if that issue was also resolved.