[teoman]

Aaa to the best of my knowledge (which is not much) lean burn doest really run hotter.

Because of the leaner conditions, the combustion is slower, so you have still burning gasses going out the exhaust hence the burning valves problem.

You can increase combustion speed with a warmr intake. Almost all chemical reactions are faster in higher temperatures.

Water will negate some of the fuel. But it could save the valves. Need to crunch some numbers if there can be any theoretical benefit.