You are correct but that is not concept of running lean or rich. Being lean or rich has to do with you trying to achieve the best stoichiometric efficiency, anotherwords find the best mixture between GASOLINE and AIR.
Being lean and rich is between oxygen and fuel, not fuel and oil, but the mixture of fuel and oil can change the mixture of oxygen and fuel. See where im going here? They are directly tied together in this wonderful 2 stroke world.
