It was low on oil but wouldn't kill the engine when running
Because it is in the CRANKING circuit, you know, the one that is not working when the engine is hot .
One usually avoids cranking a running engine, the teeth on the starter seem to object quite violently .
AFAIK the only engine with a low oil sensor that will shut down a running engine are the ones fitted to stationary engines used on generators & compressors as they are usually not monitored when in use .
Mowers almost universally have the low oil sensor on the cranking circuit.
In particular it stops idiots in showrooms cranking display mowers with no oil in them and similar for the brain dead who only read the manual after they have destroyed their new engines by starting them up without checking some one has put the oil in them.