All of the stop buttons a lift operator has access to are designed to be used any time and stop the lift safely. Similarly, lifts which need a certain amount of time between stops for the rope to settle have that built in. An operator cannot start the lift until that set time has passed.
The lift operator title is a bit of a misnomer. People in that position are trained in very basic operation and customer service.
The only way I could see a lift operator being at fault is if something was clearly wrong with the lift and they failed to alert lift maintenance. Lifties are trained to call for help when they get faults or problems. If human error is found to be involved, it is more likely to be on the maintenance side than lift operators.