I don't think the lambda is used for idle and starting and as I understand things the ECU doesn't use it about a certain engine steep near full throttle. I'm not sure how an ECU would detect a dud lambda sensor apart from a full open/short circuit. You could try just disconnecting it to see what happens.
I do not know the operation of the Mitsubishi ECU, but most current ECUs use the same control method.
Starting has its own fuel map and no throttle used. There is an idle air control valve (IACV) which allows air into the throttle bodies below the butterfly.
The ECU at idle senses RPM and opens/closes the IACV to reach the target idle RPM where temperature etc. as in normal maps is used.
Typically narrowband O2 sensors are used at relatively low TP and RPM for fuel efficiency, pollution and the like. It aims for an air fuel ratio of 14.7 (Stoich) and being a narrowband sensor, that is all it can detect - rich or lean, not how rich or lean.
Once the RPM and TP get higher, the mapping switches to Alpha-N, which is based upon TP and RPM plus temperatures, air pressure, rate of TP change and more.
This does not help solve your problem, but IMO don't worry about the O2 sensor as it is not part of the mapping/control at the TPs where you are having problems.
It could be as simple as pinched fuel line, dirty fuel filter or even air not getting into the tank fast enough to let the fuel flow well enough to the injectors.
The 15M, 5AM, 59M refer to Magneti Marelli ECU types. The Lonelec cable kit, which is brilliant, for these ECUs connects to the 3 pin (AKA FIAT - the car brand) diagnostic connector. I am 99.999999999999% sure that this will not suit the Mitsu ECU, even if you had suitable software.
Similarly, the various listed software in my guide is for Magneti Marelli ECUs only.
Alexaussi2 - from your "name" I am guessing you are in Australia - if so, send me an email at yellowducati at me dot com