I think you have been ambitious.

You will arrive at Tom Bradley International Terminal.

You need to clear immigration. The queue can be lengthy.

You need to wait for your bags.

You need to join the queue for customs. It can take as much as 15 minutes.

You need to walk to the Southwest Terminal (or wait for the bus to take you round).

You need to check your bags in.

You need to clear security. The security line can be quite long in the Southwest Terminal.

You need to walk to your gate.

A lot has to go very right for you to make that transfer in 2 hours and 20 minutes. You can't interline on WN, so they take no responsibility should you fail to arrive on time. I would be more confident if you only had carry on luggage.