running lean and engine damage

Lean is more oxygen. The more you have, the hotter the flame. Theres still enuff fuel (Gasoline) to burn, but when the ratio is off, the flame burns hotter. More fuel in the ratio towards rich, less heat.
Heat is power when the chemical conversion takes place from liquid to gas. Some poeple tune the cars via exhaust temp gauges in the header tube to a certain temp AND not as high of as a temp as possible.

Less fuel and/or more air may create more heat, but the balance of the ratio makes less power if it is to lean.
For us street guys, as long as the exhaust isn't puffing black/making your eyes water or nose cringe and/or the best times at the track are achieved.