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Hello and welcome to JustAnswer!
I see that your question has been up for an extended time without a response and while although this vehicle isn't in my area of greatest expertise I would like to try to help.
There are quite a few things she could have going on. The first thing I would recommend is checking for fault codes. If there is a sensor issue there is a good chance a code will be set that will aid in diagnosis. If no one has a code reader or scan tool available you can have the codes read for free at most large parts stores like Autozone.
The problem could be related to the throttle body, mass airflow sensor, leaking fuel injectors or a leaking fuel pump check valve, the fuel pump resistor, etc. A bad cam or crank sensor would usually cause either a no start situation or it would eventually start with a long crank time, it's possible that it could have a bad cam or crank sensor but not as likely. A knock sensor really couldn't cause a problem like she is having.
Try cracking the throttle open and see if it helps starting. If it does help then the throttle body or fuel issues are more likely.
Thank you for your time and detailed reply! I do have a question for you regarding a fuel related concern. When this issue arises, holding the start button down will keep the car running. If it was fuel related, I'm not sure I see how holding the button down would keep it running? Thats why I leaned toward electical/sensor related. While the start button is continuously held during these situations, it runs 100% normal, without orugh idle or rpm loss.
Another question...can you have fault codes with receiving a warning light?
Thank you for looking into this and offering your help. Lexus gives her the obvious (and understandable) answer of "you have to bring it in when it's experiencing the issue or we cant help." Of course, in this scenario, if she's experiencing the issue the car wont start and she cant bring it in! lol