LoDoun - Welcome to FlyerTalk!
Although some hotel locations in Los Angeles lend themselves to easy public transportation access, the Four Seasons is not one of them.
I would suggest a shared van transfer (which I used a couple of months ago). Either Prime Time Shuttle or SuperShuttle would charge you about $17.00 (plus tip) each direction, from the airport direct to the FS.
http://www.primetimeshuttle.com/SoCal.htm
http://supershuttle.com/htm/cities/lax.htm