That depends. If you are going to use this razor everyday then probably not.

OTOH, some people oil their blades after every use.

A little oil on the pivot from time to time will not hurt.

If you oil your blade be sure it is dry before doing so. All razors should be air dried after using. Most users strop on linen and leather after each use and then air dry.

If you live in Houston you have humidity: If you live in El Paso then not so much. I would not store the razor in the bath.

The type of oil is often debated. Gun oil, mineral oil and commercial lubricating oil will work.