I checked the programming specification. For normal programming 2.0V VDD is enough. But for Bulk Erase 3.0V are required. Assuming the LPT outputs 3.3V logiv level and subtract the voltage drop of the diodes - around 0.7V - we are at 2.6V which is too less for erasing the device and hence programming will fail.
Regarding pin inverting:
Since the LPT pins directly control the programming lines of the PIC, none of the pins need to be inverted.
I would not use this programmer or at least use an external 5V power supply to get stable operation.