can't help with documents, but my basic understanding is that the lambda detects oxygen levels in the exhaust gas, if it senses too much O2, more fuel is added by the ECU (less fuel if too little O2). The optimal O2 level is based on what the CAT converter requires. The CAT only works when hot, so i suspect lambda readings are not considered by the ECU until everything hot enough (hence car OK when cold). With a broken/failed lambda sensor, wrong/no signal is sent to the ECU and, from your symptoms, the ECU over-fuels (fluffy/misfire at low throttle). Also accounts for rev hunting as the ECU is looking for a signal that's not there. At high/full throttle ECU is delivering max power/fuel so the car runs and responds as normal.