Have the identical problem, except mine is an '07 LX 470. There is a thread over at the LX Board, but not the detail as here. Several people have posted however.
Never had a stalling issue before this very hot summer. This has happened twice--First, backing a motorcycle trailer into my driveway after a 120 mile drive through the desert. Second, getting off the freeway (again with a motorcycle trailer) after a 120 mile drive through the desert. Both times the vehicle stopped dead. I tried to re-start, and it rand roughly (like the old 1970's cars with the first emission control devices that would "diesel" after the car was turned off. This would go on for about 10 seconds and the truck would die. Wait about 10 minutes, started right up.
The first time, I took the truck to Larry Miller Lexus here in Salt Lake. They ran a full computer check which (naturally) came up with nothing. However, the service writer told me that mine was the third one they had heard about that had had the problem. One was driving out of Vegas, and the other St. George in Southern Utah. No explanation, other than it sounded to him like vapor lock (which is rare in fuel-injected vehicles).
The second time, although it started, about 5 minutes later the situation repeated itself.
Here are the parameters:
No prior incidents.
76,000 miles on the truck
1/4 full gas tank
Vehicle operating at essentially idle speed when stalls
Air conditioner on.
Pulling trailer --400 lbs loaded (query--could it be an electrical glitch at the hitch? Just thinking out loud)
Good gas (bought from the same station for 4 years)--premium.
After initial start-up, engine runs very rough (knocking and rattling around 600-800 rpm) for about 10 seconds and then dies.
After about 10 minutes, starts back up and runs with no problem.
A couple of thoughts--First, I suspect it is hot temperature-related (obviously) and I think wear-related, since it seems to be a pretty new issue in the older, higher-mileage 2006-07 vehicles. Second, I doubt if it is related to the cats, or we would see it much more often as time went on. Third, it is not related to the starter, battery, or ECU. I suspect it is the cam thing, fuel pump (a wear item), gas cap or vapor control system.
In addition, it is clearly a safety issue. The first time it happened, I blocked my residential street. The second time, I blocked a freeway offramp. So I am going to write to NHTSA and file a formal safety notice. I recommend that all of you do as well. I will post the link after I do.
Second, I am going to go back to the dealer tomorrow with these TSBs and the posts and ask them to investigate with Lexus US and Toyota US. I love the truck and want to get to the bottom of the problem. These vehicles are used all over the Middle East and Africa, so they are used to really hot weather.
If it happens again, I am going to vent the gas cap, pull out and re-insert the key, turn off the air conditioner, say some Hail Marys, etc., and see if it makes a difference or can narrow this problem down.
This should be a known problem and known fix. We just have to find out what it is.