I can't think of any jokes today so I'll just remind you that tools that don't get used often enough tend to grow rusty and start to sqeek.
Seriously now, The solution depends on why the squeek is there. Even tho expensive, thius may still be qa production item and is assembled with metal hardware and/or hidden bolts. Those bolts may have simply loosened up over time, ( I can't think how that would happen either) and there would then be movement between wood/wood and between wood/metal. If so, then finding the caps, exposing the bolts, and tightening them may solve the problem.
I don't think that I would use graphite. That would be a rather dirty practical joke in and of itself, since you would find black graphit stains on all your bedclothes and sheets.
If the kind of joint asks for lubrication to hide the squeek instead, I would find spray cans of Boshield B-9 or Slip-it which are available at woodworking stores and are thin spray waxes. You might need to drill a tiny hole the size of a swizzlestick at the joint to insert the spray extension tube and get planty of the wax down inside the joint.
Another option would be for a good wood worker to spread the joints apart and glue them tight back together with clamps. Of course, if you have already filled the wood pores with wax, he would then need to sand and scrape to remove that wax or suck it out with naphtha to allow the glue to get into wood pores and get a good grip to tighten up the joints.
If it is a glue failure and yuou are sure of that, there are glues ( One is called Chairlok) that can be seeped into the joint and will swell the wood while firming the joint up.
All of the above after my rusty tool comment are serious suggestions, not jokes. So after all this talk of wood, bolts, wax, lubrication, etc, aren't you glad for the internet?
Excellence is its own reward!