Lexus Troubleshooting Questions? Ask a Lexus Expert
Do you have a volt meter to do some testing?
It seems the alternator is bad based on the symptoms. You would have to jump start the car and while idling test the voltage at the battery. You should see any where from 13.5 volts to 14.5 volts if alternator is working. Anything less than 13 volts your alternator is not working.
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