"but the interesting observation is, retarding or advancing ignition for a given load and engine rpm point, i find that lambda actually changes even for the same fueling. retarded ignition gives richer readings but advanced values gives leaner readings"
timing retard will have higher egt and more unburnt charge (or higher O2 content) which registers rich on lambda. timing advance on the other hand will have lower egt and less unburnt charge (very low O2 level) hence lean. the lambda takes both the egt and charge O2 content for computations. that is why the readings are always taken at full warmup.
don't waste yr time as many on here, do not even have a clue on what you are knocking about.