There's nothing I could really add that's already been said here, most manufacturers recommend leaning above a certain density altitude (note not indicated altitude!) although this is often to prevent ham-fisted pilots from running the engine too lean and causing damage. 3000' or 5000' is usually the quoted figure in my experience.
I was lucky and was taught leaning, just as well as a PA38 I used to fly years ago (which I learned on) used to have regular problems with plug fouling. If it was encountered usually running the engine at 1800-2000rpm then aggressively leaning the engine to the onset of rough running fro a few seconds was enough to clear the fouled plug. Not a good idea to do it too often though, 2 or 3 attempts and then shutdown and a call to the engineer to have a look. That did happen a few times, much to the chagrin of the CFI. Otherwise it wouldn't have been too good for the engine's life I'd imagine.
The aircraft I flew (and most others since) have only had EGT guages that were u/s anyway so I was taught to lean to pear RPM then enrichen slightly. Not the most accurate but enough to avoid damage with the limited info available. There was one PA28 that had a serviceable EGT but I was so used to the RPM method that I just used that anyway.