Okay we know the problem now!!! If anyone has a GS430 and having similar problems, here is the answer! (Which I was hoping to find myself when I came here!!)
After 3 days sitting in the mechanics shop never "acting up" for them, I finally made a communication breakthrough with him. I didn't know why it was acting up for me when they came to pick up the car (for the 2nd time) and then they proceeded to take it to the shop and CHARGE THE BATTERY AGAIN!! Then sit there and wait for it to act up again!! I told him over and over it will start slowly, then each time (after DRIVING IT) and starting again it would start slower and slower 'til eventually it would just "click click click"
So after my dad already went round and round and I also thought I had explained the symptoms clearly, and 3 full days sitting in their shop, I got through to him that it needs to be DRIVEN in order for the battery to run down. Here he was sitting there waiting for some intermittent thing to happen in between driving it, to draw down the battery. I said NOOOOOOOO it has to be driven, of course its not going ot act up with a full battery just sitting there with their testers on it.
Ahhhhh so finally. he took it home overnight and sure enough it cranked slower nad slower 'til it died on him in the morning. Oh NOW they see it is the alternator after all!!! their static testing would have never shown it to be hte alternator since it is too sophisticated and wily I guess. So they went to get a new alternator and that one is on backorder with Lexus, so they found one in NY which should be here Monday (tomorrow) and finally get my car back and working after a week in their shop, plus in their the week before. 3 weekends in a row carless.
LExus would have never found this problem either since htey do their testing the same way. we had already taken it to them over a year ago with the same prob but ended up with a new battery. well that only bought us time. this was pre owned as well so I bet the new owner had traded it in for hte same mysterious problem.
WELL ITS NOT MYSTERIOUS ANYMORE!!! I hope anyone running into the same issues finds this nad can tell their mechanic that is IS the alternator!!