A set (throttle, prop, mixture) of PMA cables for a M20 is said to be around $1000.
The TB20 propeller pitch control cable is €442 + VAT 
So the original Q is very valid. There may be nothing wrong with it. However, we can probably extract it at the Annual and get inside it properly.
Most likely it got tight because rain water gets in at the front – as the above pic shows. It’s a crap design; there should be some sort of rubber shroud. However, this seems common in GA; the other day I saw a plane with a totally exposed alternator right at the front. The alternator must just fill up with water every time it rains.
I happened to be talking to a chap with hire boats at a marina. And he said that since starting yearly lubrication of the control box / cables they’ve not had any failures.
Although they pulled the unit off, and used what looked to be a length of hose which they filled with oil then put in a small airline at low pressure to flush them right through each cable. It was not a quick process.
I don’t believe anyone pretends there is a permanent solution. But as with so much in aviation maintenance, if you can safely get another 10 years out of something, why not? And, as I said, the labour cost can be really substantial getting access to some cables.
I maintain my plane on a money-no-object basis (it is the cheapest way to run a plane) but will still grease a control cable, especially a non-critical one for the heater
I am changing my prop governor cable at the next annual. It has been running against some part of the engine, and the outer sheath has come off in places.
It depends on what type of outer the cable has, if it is a Nylon lined then it is unlikely that lubrication is a long term option.
Older aircraft have cables that are a metal coil outer with the cable running through the centre, these can benefit from lubrication, Alioth suggests LPS-2 and I would not disagree however I have used Mouse Milk to free these cables if they are very difficult to move.
Never had a problem with cables going under the cowling, but our trim cable’s orifices are quite exposed at the rear of the aircraft, and and moisture can have a tendency to get in leading to the trim getting excessively stiff. Since I’ve owned the plane I’ve been squirting it with LPS-2 on every 6 monthly check, and the problem has never recurred. LPS-2 seems to wick down the cable pretty well.
After almost 2 months undergoing paint strip and repaint, the throttle cable had very little movement. It was removed, cleaned, greased, and refitted. No problems so far. A short cable on an O200 in a Bolkow Junior.
To some extent this depends. You can get semi-seized cables because some dirt got in at one end. Or you can have a cable with a solid rod portion at one end and this rod started to corrode; this is not unusual on throttle and mixture cables. Lubrication is a good way to deal with this and get another say 10 years out of it.
My cable experience is mainly marine orientated.
I posted the tools above in a hurry, but agree with the guys about the fact it may be time to replace.
It’s a common conversation where a huge effort to lubricate a cable does sometimes provide relief but is short lived. It’s a boating winter job and usually ends up on cable replacement, maybe the following winter.
During the lubrication times it’s either ineffective or slightly effective with lubricant constantly weeping from the cable ends.
A_and_C wrote:
when they become stiff it is usually time to replace the whole assembly
That’s my feeling, too. If it has become stiff, it probably means the reciprocating motion of the inner cable has dragged enough dirt from the ends inside the sheath. Short of replacing the whole thing, one will need to remove the inner cable and rinse the hole thoroughly.
