Leaning a Carbureted Lycoming or Continetal past Peak

If your objective is to lean of peak (LOP) then lean until the engine gets rough. However, I see no purpose for this. First outline the problem and the solution:

1. operate at best power to climb over that mountain, or maximize speed, or, 

2. operate at the lowest specific fuel consumption to maximize range and minimize $, or,

3. operate the engine in a manner that minimizes lead deposit build-up.

Objective 2 just happens to be somewhere on the backside of an egt curve.

Objective 3 is indeterminate as it depends on the engine and power setting but as a general rule leaner is generally better up to a point.

If your objective is 2 then very SLOWLY lean until you feel a slight roughness and then enrichen slightly to remove the roughness. You are probably very close to lowest specific fuel consumption. So how does this relate to LOP? At least one cylinder is LOP.  EGT readings show some cylinders somewhat hotter egt (closer to peak) or somewhat lower egt (before peak, or after peak). All very confusing display for the pilot and somewhat worthless data.

To add the the EGT confusion, there is no standard temperature drop past Peak EGT  that produces the leanest operation without engine roughness. And it is engine roughness that limits lean operation, not some exhaust temperature reading. So lean to engine roughness and then enrichen slightly.

engine roughness defined for this purpose: A very slight and non-regular vibration pulse that your passenger probably won't notice. It is NOT a "rough engine"

All leaning suggested above is at power settings below 75% power.