Without wishing to start yet another massive thread, it's important to understand a little bit about engine efficiency as applicable to the spamcan market.
For the last few years I have been flying an aircraft whose engine is operated precisely lean of peak (LOP) and I have had an accurate flowmeter - usually better than 1% when correctly calibrated etc. So I knew I had 2 hrs and 35 mins before the juice ran out; I also knew I would have 2:10 at the planned destination (corrected dynamically for current ground speed) and this would be right within a few mins. I have not flown spamcans at all - until recently when doing the IR and this reminded me of the dodgy fuel practices that prevail in the flight training business where just about nobody (including the instructors) understands what they are doing.
Normally, spamcans are flown well rich of peak (ROP). This wastes fuel massively (up to 30% for the same speed obtained otherwise) but has two advantages:
a) the combustion is cooler, which is good for the heavy handed flying that takes place in that business
b) every cylinder is getting more fuel than it needs which circumvents the poor fuel/air distribution that is common in carburetted engines (if you try to get this just right, the engine vibrates too much because some pots are making more power than others)
The trouble with flying massively ROP is that nobody actually knows the flow rate. It isn't in the POH. In there (PA28-161) you get typically two lots of figures: "best power" and "best economy".
BP is about 100F ROP. This isn't quite the full rich position most spamcans fly at, but nobody knows where it is on the lever position.
BE is peak EGT, close to the best efficiency, but most carb engines can't make peak EGT without vibrating (reason above)
So, the traditional way, taught here and everywhere, is that you lean until
a) the engine gets a bit rough, or
b) until the power drops off
whichever occurs first, and then you go a bit rich and check the carb heat still works
With carb engines, a) usually occurs first but nobody knows the actual flow rate because .... well.... the engine will get rough when the leanest cylinder goes LOP and this depends on how badly matched the fuel and air delivery is ... b) is a good indicator of the peak-EGT point but most spamcans can't get to it for reason given above.
So, most people have no idea of the flow rate, not better than +/- 20% of the POH figures.
So, the smarter people fly with massive reserves; say 3 hrs max endurance on a plane which could actually do 5:30 if optimal. Those who are a bit too smart and try to calculate things properly (as they have been taught) are likely to end up in a field - because nobody told them the actual flow rate is anything up to 20% out. Or they end up in somebody's loft and the CAA takes them to court, but the CAA loses because it is "revealed" (shock horror, absolutely nobody had any idea) that this pilot was only following what is standard practice in the training business.
Instructors often get to know a particular plane really well (obviously) and they know just how far they can push it, and they often go very close to the edge, but this is no good to others.
So, to briefly answer the original question, leaning is OK anytime en route or in descent. Not in a max-perf climb when all should be fully forward.
A prohibition on leaning below say 3000ft is standard school/club practice (for reasons given above) but it doesn't relate to engine reality.