The correct answer is B) Ahead throttle will close. If both the main and standby lube oil pumps fail on a geared main propulsion turbine operating at full sea speed, the loss of lube oil pressure will cause the ahead throttle to automatically close, shutting down the turbine. This is a standard safety feature designed to prevent catastrophic damage to the turbine bearings and other critical components due to lack of lubrication. The other answer choices are incorrect because: A) Vacuum would not be immediately lost, C) The lube oil sump would not overflow, and D) The HP turbine bearings would overheat, but this is a consequence of the loss of lubrication, not the first thing that happens.