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The gearbox on our equivalent multi-point locking system failed due to a moving part (a small cast toothed-bar) breaking. Finding a replacement took a bit of googling, measuring, and talking to someone at a locksmith on the phone while they measured up a replacement, but I did find one. I used silicone spray to get everything running smoothly, but having recently used graphite on our front door cylinder (grinding a pencil lead into the keyhole) I can vouch for that making everything very smooth.
As @ElephantBreath said, if the cylinder is gritty and rough to turn the key, graphite is recommended for lubricating it, but flush out with something that's not going to set, or collect more muck in the future.
Exactly. If you remove a short M4 machine screw from the handle area or next to a hook, put it back in.
If your mechanism has screws holding the gearboxes onto the face plate, leave them in place and remove the complete strip as one. If after cleaning and lube, it's still poor, remove the centre gearbox and see if its the centre or hook gearboxes. If its the centre, you can get replacements for some, but not all.
Here's an
Top. Avocet mechanisms with the gearbox rivitted on.
Middle. ERA mechanism with gearbox screwed on
Bottom. ERA gearbox.