Why would you NOT lean on takeoff with a Lycoming engine? There is an excellent question/answer on leaning here. However what I have not yet understood is why one would NOT lean for takeoff below 3000 feet? Why does the Lycoming Service Directive 1497A/B still say to use Full Rich on takeoff? 

Is it not right that a leaned engine is producing its highest power output and would you not want the highest power output on takeoff?
You are correct - you do want highest power.  But you also want an engine that doesn't overheat and destroy itself.  

Your initial climb-out is at an airspeed considerably less than cruising speed so you have less air flowing through the cylinder cooling fins.  To compensate for this, flying full rich keep the combustion gasses cooler during the climb-out.  

When you reach cruising altitude and level off, you may lean it out in accordance with the engine manufacturer's recommendations.

This "full rich on takeoff" procedure is not limited to Lycoming engines, either.  TCM Continental and even the older Pratt and Whitney radials also go full rich on takeoff. It is close to a universal procedure for piston powered aircraft engines.