FWIW, the clutch kits I usually buy come with a small packet of spline grease not unlike the little packets that are usually lined up on a rack at the parts store counter. I use it, figuring that the clutch manufacturer would supply an appropriate grease. I just squirted it on my fingers and put an almost imperceptible amount on the splines. Failing that, I wold hesitate to use a small amount of any good synthetic grease. The disk should slide pretty freely on the splines-I've always thought that the main purpose of greasing was to prevent the disk from sticking in disuse.
I've never lubricated the release bearing pivots themselves. They don't move a lot, the release bearing can run hot, and with the heat in mind it's a bit too close to the friction surface for my comfort.
The bearing forks I've handled had a self-lubricating bronze bushing in them. I usually buy a replacement bushing if I don't have one on hand, but have rarely needed to change one.
I should also mention that most of my clutch experience is related to one particular make of car, but a lot of the basic premises are the same.
