I hesitate to be the party pooper, but please take into account that introducing oil or penetrating oil into the public water supply (even if it is only your own individual supply) is illegal, and carries quite stiff penalties. It's not just jobsworth pedanticosity, even small quantities of hydrocarbons will taint your supply and you will taste them.
Materials in contact with drinking water must have passed through the Water Research Council approval program and be WRc approved.
There are food grade lubricants about – Rocol make one called Foodlube which can be bought in an toothpaste tube, but to the best of my knowledge it doesn't have WRc certification.
The materials used by the water companies have to be DWI (Drinking Water Inspectorate) approved, which is even more stringent to ensure that even small traces of deleterious substances are kept away from the public water supply.
Best answer by far is as suggested – get your local Water Supply Authority to check over their stopcock, so you or they can isolate your supply. Then remove and replace the offending consumer side valve.
You may have difficulty retaining command of whether a water meter is fitted or not, depending on the local policy.
Good luck!