Clean the bumslide out of it and lubricate with SAE 30 lawnmower oil as recommended by Webley. It's a phospher bronze piston ring and it relies on the viscosity of the oil to seal. They also diesel a tiny bit in normal use and are designed to do so.
The breech seal will need a good soaking in oil to revive it , just put a couple of drops on the seal and leave upright overnight. If the seal won't revive easily. Put some drops of cigarette lighter fluid on it and let it soak in before oiling it again.
If you must lubricate the piston body, squirt some dry graphite powder into the cocking slot and work the piston to and fro a few times. Cocking linkages , barrel pivot and stirrup pivot will benefit from a drop or so of 3 in 1 type oil.

The lock screw for the pivot screw is a special and a real barsteward to duplicate. Chambers and Knibbs sometimes have them but I believe they are both out of stock.


Hope that helps