Grouse, I didn't know there was a train to Hollywood. Since your going to TPE you're probably checking bags but I wanted to remind you that storage lockers are now unaavailable at LAX for security reasons. If you've never been to Beverly Hills and you have an interest in it I would take a taxi or shuttle to Rodeo Drive. My first choice would be to take a bus/shuttrle/taxi to Venice Beach and spend some time there. Frtom Venice its an easy taxi to Santa Monica. You can visit SM beach, the SM Pier, and Third Street Promenade for lunch or dinner. If you do wind up at In-And-Out Burger get a double-double.