The catalyst converts these harmful elements into gasses that are not harmful, ....

Correction - less harmful. Just a bit more CO2. Water vapour is fine. :-)

Lambda 1 is the term we use to refer to a chemically correct air/fuel mixture of 14.7:1. This is also known as stoichiometric.

For the purposes of MOT a vehicle must obtain a lambda reading of 0.97 to 1.03 to pass. It will fail the test if the lambda reading is outside these limits.

Petrol engines emit carbon monoxide (CO) and hydrocarbons (HC). The catalyst converts these harmful elements into gasses that are not harmful, and are subject to maximum limits on the MOT test. An engine which is running correctly with a catalyst in good condition will easily pass the MOT in this respect.

Diesel engine vehicles are checked using a smokemeter which measures smoke density. It does not (currently) measure indiviual pollutants within the smoke. I dearsay one day it will, so watch this space.

You missed out NOX(nitrous oxides)emitted by both petrol and diesels-these(CO,HC & NOX) are reduced by a three-way catalyst. CO and HC were removed by a two way catalyst(oxidising catalyst)-used in the early days. NOX figures are not YET required for MOT.