Thai Airways has a limited presence at LAX, namely four weekly B777 flights to Seoul, South Korea. Formerly, there had been a non-stop flight to Bangkok in an A340-500, which at the time was one of the longest scheduled airline flights in the world: Sixteen to eighteen hours in the air. That flight was discontinued in 2012, and marked the departure of half of the A340-500 operations* at LAX. The replacement flight to Seoul does continue on to Bangkok, and has recently been upgraded from a B777-200ER to a B777-300ER. There has been talk of Thai bringing an A380 to LAX, but so far all I've heard is talk.
Something that has not been a regular sight at LAX is a B744 in Thai colors. We had one pass through a couple of weeks ago, though -- on its way to Mohave. Mohave is one of the places where airliners get parked; Victorville, California, is another. There are also several locations in Arizona where airlines and leasing companies store aircraft. Is this aircraft going into storage? I don't know; there's not much information on the web about Thai retiring its B744s, although some other types are known to be on the way out and many other airlines are parking their B747-400s. Since most of the airports that host parked airliners also offer heavy maintenance facilities, it could be that this airplane will return to the skies in the not-too-distant future.
Besides this Thai B744, I've also recently seen an Air New Zealand B744 and a KLM MD-11 pass through LAX on their way to the desert.
* - The other A345 user at LAX was Singapore, who flew theirs non-stop to Singapore, a similarly long (16-17 hours) flight that has since been discontinued in favor of a flight to Tokyo that then continues on to Singapore. We no longer see A345s on a regular basis at LAX; both Singapore and Thai have dropped the type from their fleets. Etihad brought one in during their first weeks of operation here earlier this summer, but they now use B777s.
