You are correct, the answer is B) Excessive lube oil consumption. A leak in the lube oil cooler would allow seawater to enter the lubrication system, leading to excessive lube oil consumption as the contaminated oil is used up more rapidly. This is the primary indication of a lube oil cooler leak while the vessel is underway. The other options are incorrect because: A) Contamination of the lube oil could have other causes beyond a cooler leak, C) Corrosion of journals and bearings is more likely due to insufficient lubrication, and D) Excessive water discharge from the purifier could have multiple causes beyond a cooler leak.