Yesterday, the sensor (which was the original part that failed on our hot water heater) finally arrived. That was eight days after I initially contacted the company that manages the extended warranty for Lowe's. I am told that the valve is going to arrive tomorrow and that they will finally fix the damned thing.
I've also been told that this was "expedited". If this was what "expedited" service is like, God forbid that we should get some other kind.