Ok, it's fixed, and here is the update.
First of all, thanks so much to John for recommending ATRA!
I first took the car to a transmission place that I went to last year. They wanted $3200 to rebuild the tranny!
I searched for ATRA members in my area, and found another place. In the end, I went there, and only paid $1700 for the rebuild!
Both places said that it needed a rebuild. That these Lexus transmissions were one of the Lexus weaknesses.
There were metal shavings/dust that was sticking to the magnets in the transmission pan.
When the transmission was apart, I took a look at all the damage. There were chipped gears. And a cyndrilic object that had metal chewed off the outside edges at the end. About 4 inches in diameter, and 6 inches in length. Welds holding gears that had loosened. Lots of damage! No wonder it didn't want to move.
He said it looked like the transmission had already been replaced. And that one gasket had been put on the wrong side of an object. That was the reason it self destructed. So, from what he told me, it was an off the shelf rebuilt transmission. Put together wrong. And slowly self destructed over time.
Now that it's replaced, the car sounds different. I'd thought after I bought the car, that it sounded different from my old Camry. There was always some noise when I accelerated, and coasted. Now, the Lexus sounds more like my Camry did. It's quieter.
Fortunately, there was no reason to change any of the electronic sensors, which would have been extra. I'd had no lights coming up on the dash.
One thing I learned when I contacted the Lexus dealership. These transmissions require the Toyota number 4 transmission fluid. Regular Dextron 3, will cause the transmission to self destruct over time. The Lexus parts guy said that Jiffy Lube had indirectly been one of their best customers. Because they kept causing so many failed transmissions by using Dextron 3.
So, I hope this helps anyone else who has issues with their Lexus. Good luck!