Do you have to lubricate the shock strut?
Oleo struts and brakes used on light aircraft use MIL-H-5606H hydraulic fluid (the red stuff) as the internal damping agent/lubricant (be sure to check the manual anyway). It's a normal practice to clean the exposed chrome of the shock strut (it should be done with the tail held down to extend the strut all the way) with a clean cloth, then wiping it with a cloth with a little bit of 5606 to leave just a very light film to help lube the scraper and seals the next time the strut compresses (once that's done there is the film of internal fluid left behind by the seals).

The biggest enemy of oleo struts is silica particles (which are very hard) from outdoor dust which sticks to the chrome surface because of the fluid film left behind by the internal seals.  The silica collects in the seal cartridge and acts like lapping compound, accelerating wear (this is why desert operations are the toughest environment overall on any airplane).  

As the strut ages and the seals wear and slowly start to leave behind more fluid each time the strut extends, dust collects faster and the whole process speeds up, so the strut should be kept clean as much as possible depending on how dusty the local environment is.

If it's your own plane, you should learn to do the published procedure yourself, because nobody else is going to do it between annuals.  If you're renting the plane, that's the owner's problem, and you just do your normal walkaround inspection.