I am also having this problem. Car was built Feb 1996.
Research suggests that...
I quoted a new ECU at about $2,600 (not sure if that's installed or inc GST or what)
I sure would like to learn it's not the ECU and that one of the above fixes would work (decarbonising the intake or a crack in the air intake after the air flow sensor for example) but I'm sure that Lexus will charge me a million dollars to do that as well. Problem is I trust no mechanics to know what they are doing these days and feel like whenever I go to one I am a lamb being lead to slaughter.
One clue is that if I shut the engine down and restart it it runs just fine and idles nicely. The front O2 sensors are new but the rear O2 sensors (at the cat) are original. I have 190k on the car so far. I bought it less than a month ago from Sydney and drove it back to Adelaide then drove from Adelaide to the Gold Coast and back over the last 2 weeks. It stalled in every town if I let it. Fortunately I am used to driving rough idling V8s and when I couldn't be bothered switching it off then on again every time I slowed for a town I just "two-footed" it to get me through. Very uncivilized.
If anyone has any suggestions... 041 505 2020
Thanks
Bill