Actually it will happily run with a disabled lambda sensor. It will just run on the programmed map. Many race cars are driven that way. Will likely not pass an MOT though 
The engine struggling up in the rpm range is likely something else and if the ECU is not logging any faults (I assume you have no DTC's if you view those with Kmanager?) then it's likely something in the 'supporting hardware'.
Heck.. Could even be an ignition coil that's perhaps not too fresh anymore and causing some misfires or similar.
Still.. The lack of a working lambda does mean you can't datalog some info.
Bye, Arno.