Thanks--had a syntax error on the year. I appreciate all the help. I am shocked a certified lexus tech AND a lexus rep cannot figure it out...or care for that matter.
It sounds like it could be something in the ecu that expands and disconnects, Then cools down and reconnects like a crack in a circuit board or something on those lines. Just a guess, I had a car back in the 80's that did this and it reminds me of my few times going down the road then WHAM totally off, disconnected, shutdown. 5 min. later it would start and I never knew when it would happen again.
I agree, it sounds like it's the ecu unit. I'm SUPRISED the lexus dealership didn't check that, but instead spent their time on the throttle body.
You say it only happens with the A/C unit on??? I wonder if the alternator is bad. The a/c electrical pull could be too much for the alternator, which kills the car. Maybe the battery is strong enough to restart the car, but once the alternator gets loaded down, it kills it again....
I'm printing the last two and marching up to the dealership--this hasn't been approached. Thanks folks.