Once you have the cylinder and crane off the frame:
1. Put 2 (or more) FIRED (empty) cases in the cylinder. This helps protect the tabs that the ejector "star" locks into.
2. Wrap some duct tape or leather around the knurled end of the ejector rod.
3. Use vise grips or pliers to grab the taped rod and grab the cylinder with your other hand (I have a special set of vise grips with an aluminum insert made to do this)
4. Turn the ejector rod CLOCKWISE (looking at it from the muzzle end of the barrel) to loosen it (it has left handed threads due to the direction the cylinder rotates)
5. Remove the rod and you can then remove all the guts of the cylinder
6. Be advised, there is a small internal tooth lock washer down in there you don't want to lose
You can them clean to your hearts content and then put it back together. The only lube you need to do is on the bearings, where the shaft goes through the crane and maybe a bit on the ejector shaft where it comes through the end of the cylinder.