The correct answer is C) Lube oil pressure. The lube oil pressure should be checked immediately after starting any diesel engine because it is a critical indicator of the engine's health and proper lubrication. Low lube oil pressure can quickly lead to engine damage if not addressed. Checking the lube oil pressure is an essential step in the engine startup procedure as outlined in the regulations and manufacturer's recommendations. The other options are not as critical to check immediately upon startup. Exhaust temperature (A), lube oil level (B), and water level in the expansion tank (D) are important to monitor, but they do not require the same urgent attention as lube oil pressure when starting up a diesel engine.