MOT - so you are located in Great Britain? If so, you may be able to get a more appropriate response about compliance with your specific regulatory regimen by posting the question on the NSX club Britain forum.
That said, lambda is a curious compliance requirement. In North America, the emissions check typically evaluates CO, Hydrocarbons and nitrogen oxides (NOX). I have never seen Lambda used as a pass - fail requirement because an engine running at a lambda of 1.0 can be dumping out lots of NOX and other nasty stuff if the catalytic converter has failed or the EGR is bunged. The fact that your tail pipe test lambda is 1.07 - 1.12 suggests that the car is running lean or you have a leak in the exhaust system. When the engine is up to operating temperature the engine should be in closed loop fuel control and your tailpipe Lambda with a tight exhaust should be close to 1.0. A high lambda definitely will not help your NOX compliance.
You did not specify the year of your car which can be significant in terms of the advice you get. OBDII came late to the UK. If you had a late spec car with OBDII you can connect a scanner to the car and monitor your O2 sensor voltages with the car in operation. This can give you a lot of guidance when things go wrong. If you have a pre OBDII car, this is not an option for you. However, whether it is a pre OBDII or OBDII car, the engine when hot should be in closed loop giving you a tail pipe lambda around 1. If it is not operating at 1 it is:
- not in closed loop or
- the closed loop control has reached its correction limits (this would normally trigger a MIL light) or
- the O2 sensors have drifted in their accuracy (essentially dead; but, haven't fallen over yet - the sensors have to be really dead to trigger a MIL) or
- because your lambda >1 you have an exhaust system leak.
Have a closer look at your pass / fail test results to see if there are some other indicators (CO, HC, NOX) which would provide more information on the reason for non compliance. Right now, given the limited information it is not obvious that more driving around to ensure the catalytic converter is hot will fix your problem.
