hey i m sorry to hear about your stroke , i m glad you okay now & you are back :)
1-the exhaust catalytic system is original to the car , if it is clogged it will act up when it heats up, the car runs better when cold since the pcm uses the maf, ect etc.. sensors to run the car cold when it gets hot the o2 sensor takes over , so if the catalytic is clogged when hot it will start to acts up , since the sensors are reading correctly but the Catalytic is not letting it breath right .
2-next will be changing fuel pump, it is rare on Lexus to go out , dont cut line , it has special adapter to test that system
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ASE Certified Technician