The correct answer is A) High vibration on the gas generator. The main reason for this is that high vibration on the gas generator is often the primary cause of a gas turbine engine shutdown. Excessive vibration can indicate issues with the rotating components, bearings, or other critical parts within the gas generator section of the turbine engine. This high vibration would trigger automatic shutdown mechanisms to protect the engine from further damage. The other options, such as high lube oil temperature, low fuel supply temperature, or low sump oil level, could potentially cause issues, but they are less likely to be the immediate cause of a sudden engine shutdown compared to the detection of high vibration.