The car seems to stop pulling at 55to60 miles an hour put it in neutral n back in drive she takesa off again

Sounds like you need to find a competent transmission shop.

Your first mistake was to listen to a parts person at Autozone and actually buy the part he or she suggested, THEY ARE NOT TRAINED TECHNICIANS! You need to take this either to the dealer or a local transmission repair shop. In Calif these parts stores can't do the testing and can't hand out advice on vehicle repair. There is a reason why a trained automotive tech makes $30.00+ per hour and they make maybe $10.00, it is called training.

Could be plug catalytic con.

Sounds like loose wiring under the dashboard.

Sounds like the same issue I had with my 2002 Discovery 2 V8. Mine used to run for about 10 minutes, then die, usually in the most inconvenient locations! The Crank sensor is in need of replacement. It sits near the exhaust downpipe (behind a heat shield) but obviously this shield isn't enough as they die after about 80,000-100,000 miles. Just get it replaced and I think your issues will solved.

o2 sensor

A bigger transaxle problem is coming soon

The avg life of a taurus/sable transaxle is 65,000 miles

You need to start with a fuel pressure gauge on the car while driving and see if the pressure is droping, you could have clogged injectors if the fuel system was the bad, please rate

Your tranny need to be repaired at once. The tranny is slipping. Some Lexus owners do have the similar problem including myself.

When it stalls, does it start back up and then die again when you put it in drive or just not start back up?