"The "let the engine cool before washing" language has been in Honda manuals for years; here's the science/why:
--When the engine heats up, so do the bearings. Hot metal expands, including the space/gap in the bearing.
--Spraying water near the hot bearings leaves a lot of moisture near and inside the gaps.
--As the bearing cools, the air pressure drops, and actually draws in water inside the bearing.
--Water trapped in the bearing causes rust to form, and eventually, the bearing will fail.
This is more likely to happen on mowers with a blade clutch, vs. those with blades bolted directing to the crankshaft.
Silicone is the best overall lube for cables; once a year is probably just fine, but if you notice them binding or getting stiff, a bit more often is better."