excaliber

Hello, bringing my car into Lexus today. Car is a 97 sc400 with 182k miles, runs great but has had a small issue for past 3 years. Every few months it will turn off after being started first thing in morning, turn right back on and then off again and then on for the rest of the day and beyond. No problem and not annoying until this past monday when it turned off while at stop light and kept turning back on but then immediately dying. Always starts up though this time around I had to have it towed.
Had serpentine belt replaced. I know the alternator might be power steering soaked, common with these cars. A throttle body cleanse stalled the issue a few times by the dealer. Any ideas on what they should check today or what service to have done? Operating on low cash and in PA so hopefully good amount of the checks might be courtesy checks. Getting loaner for the weekend so theyll have it for at least 2 days.
Thanks for help guys, my current list of questions/requests for them is below:

Check alternator (have been told by firestone its at 10v running) maybe clean oil as much as possible.
Check that they installed serpentine belt correctly as problem hasnt resurfaced since belt fixed but car only ran for a few miles since then, have been bussing it to be safe.
Check/clean throttle body and iacv.
I have check engine light but it was diagnosed as 1st bank 1st sensor O2 so not worried about that.

Anything else to check?

mecheng10

if your alternator is only putting out 10V, that is a serious problem
it should be more towards 14V

excaliber

Yea, thats what Liarstone said so thats question 1 for lexus, to check the volts, make sure they were telling the truth there. Would that cause the intermitten and then finally the full starting issue I had Monday?