2000 Lexus ES300

2000 Lexus ES300

Is there any correlation between the computer in the Lexus and the alternator and battery?

Also,
Sometimes my car won’t start or dies while idling. When I try to start it, it makes a rapid clicking noise and will start with a jump. I’ve had the battery replaced and the alternator replaced twice. Oddly, it sat on my driveway during 2 days of frigid temperatures, started immediately, but later stalled after some local driving. Any suggestions for my mechanic?