I think some cleaning kit I once had, had a tub of lube in it, which I chucked without thinking. On second thought, should I be lubing my gun after cleaning? And if so then what parts?
Usually just a tiny dab on the trigger pivots and the trigger needle where it goes into the gland. You don't want to go mad with it, especially as it can contaminate the paint job if you have soaked the gun in something.
I'm sure there will be in depth step-step guides on gaztube.
I used to dip a screwdriver in oil, wipe most of the oil off, then wipe the screwdriver on the needle behind the packing, with the trigger pulled.
I have never oiled the trigger or the push thingy the trigger pushes.