You should turn off the petrol and let the carburettor run out of petrol Turning off the tap saves the possibility of float needle not closing properly and causing the engine to flood and also possible run petrol mix out onto the garsge floor
Another good reason to rin the carby out dry is that if the mower is left for a long period with out being used at all any petrol mix left in the bowl will dry out leaving behind the oil content which does not evaprate like the petrol does. This oil can be enought o block the main jet next time you try and start the engine . . It also means you have a mix ofstale fuel and fresh fuel. It is easier to start up the engine if it has a full charge of fresh fuel in tha carby when the engine is cold ..