Lycoming are very clear in the advice on their website:
"First we must know that cruise power for Lycoming normally aspirated engines is generally considered to be 55% to 75% of the maximum power for which the engine is rated. At these power settings, the engine
may be leaned at any altitude. There has been confusion about the reference to not leaning below 5000-feet density altitude. Remember that this reference only applies to those power settings above the cruise range — those normally used for takeoff and climb. Once cruise power has been set, leaning to best economy should be standard procedure as damage to the engine will not occur from leaning at cruise power settings."
(The bold is in the original document - I didn't add it.)
So there you have it - it's not leaning that damages the engine, it's leaning
at high power that does it.
Here's the document on the Lycoming website that explains this. If you go up a level to the "Operation" section there's plenty of other useful documents too.
I personally think there's no excuse for flying schools not teaching this - I myself was never taught, and have had to educate myself by looking for reliable sources of information such as this document. I quickly realised that there's so much myth around this subject that it's almost useless asking an instructor because they're just as likely to give completely wrong advice. This thread has just confirmed my suspicions!
Sure, if done badly it can damage the engine - but all the other controls can cause problems if mishandled as well. Think about it: misusing the elevators can break an aircraft... so better not move the control column back or forth. Too much rudder during a stall will cause a spin, so we'd better leave the rudder neutral all the time as well. Come to think of it, the ailerons can put you into a spiral dive - best not tamper with those while you're flying either
"the engineers tell me its a bad idea and shags the engine"
I suspect there's some distorted logic here. What happens (I suspect) is this:
1) An engineer discovers a shagged engine.
2) Engineer asks the owner "do you lean your engine?"
3) Owner says "yes".
4) Engineer concludes that leaning damages the engine.
But the engineer doesn't consider the large number of pilots who lean their engine correctly and don't suffer damage (they also don't suffer stuck valves, oily plugs, etc. etc). All the engineer really remembers is this one pilot who leans aggressively at high power and knackers the engine.
I'm certainly not saying all engineers are wrong - just that it only takes one owner to misinterpret what the engineer says and pass on the misinformation, and thus a myth is born.