What about taking the LAX/Union Station Flyaway to Union Station and then the Red Line to Hollywood/Western station? The Flyaway bus is $7 each way card or cash and will cut down transit time by 65%.

But if you do decide on eating at a Thai restaurant in the LAX area, then I suggest going to Thai Dishes on Aviation Blvd. since it can be reached easily by the free "G" line bus to the Aviation Station stop and then south on foot to the restaurant.