There is not much lubrication used on most shutters.
Mostly a very small amount of fine oil, like watch oil, used
on the bearings of the gears in the speed regulator
escapement. In the USA one can get suitable synthetic
(silicon) oil at hobby shops that model railroad materials.
Another oil is Nyoil, a Google search will find it. The oil
is applied with a bit of wire or a very fine brush. Some
sliding parts, mostly speed adjusting rings, etc, sometimes
are lubricated with light silicon grease. If the shutter is
on speed without lubricant I would leave it that way.
  Silicon lubricants have the properties of not wandering,
operating over very large temperature ranges, and not
thickening up with time. All lubricants tend to trap dust
over time.
  Never use powdered graphite in a shutter and never
lubricate shutter blades.