I have been experiencing the same thing on my 2004 LS430. It happened for the first time about a year ago, but the check engine light would never come on and the repair shop told me the same thing: they could not diagnose it unless they could experience it or get a check engine code. Just last week, it became impossible and dangerous to drive and the check engine light finally came on and I brought it in to the repair shop.
They said that there were several codes recorded but that they thought the air flow sensor was bad.
They replaced it, but it stalled again on me yesterday so I am back to the drawing board.