After looking at all the bits I have accumulated over the years I came to the following conclusions: - Grease'n oil lubrication is the accepted compromise to keep some lubricant inside the gearbox, but it is not really a good thing. Have a look at these three main shafts: All of them have scoring marks from running inadequately lubricated in the sleeve gear. Measuring them up showed me that they were significantly worn, especially at the outer end.
- The sleeve gears I had showed a similar trend, with their bore being significantly larger at the outer end.
- Altogether the running clearance in the sleeve gear, which I am told was originally 5 thou had thus increased to 10 or 15 thou. This is not only a clearance where the whole setup can no longer work as a hydrodynamic bearing, but also the mainshaft can no longer keep the sleeve gear well enough aligned for the ball or roller bearing holding the latter to work for any significant mileage.
- besides that, the clutch splines on most of these shafts are a bit worn, which means the clutch centre will not seat properly, and will continue to wear the splines out.

I made some enquiries about hard chroming or metal spraying the portion of the shaft that goes through the sleeve gear, but gave that up because of the worn splines and some other issues.
So I sat down and made a drawing.
Which made me realise that it was not impossible to make such a shaft by my own means, but a demanding task...

So I obtained a metre of 18CrNiMo7-6 case hardening steel and set to work. First job was to drill the bore for the clutch actuating rod. You need to drill from two sides, but only after VERY carefully centre boring the respective end. If you start drilling only slightly out of centre, your drill will be way out when it meets the bore from the other end. And you need to drill quite gently, removing the drill every few millimetres to clear the swarf - you don't want a broken drill stuck in your piece of work... Actually, this is why I did this tedious job up front, so only a piece of material would be lost in case...

Rough turning the job was nothing special, save for the fact that the material produced long hot and sharp swarf which - in the best case as seen here - wrapped up around the work. Sometimes it would curl up and point in my direction...

This is how it looked then.

I then encased the bit in a sand-filled piece of steel tube and annealed for two hours it in my wife's pottery kiln at 600° to relieve any potential stress in the material in the hope of thus minimising the distortion in the hardening process.

A measuring session before and after showed no measurable difference, so I could have saved this effort...

Before having a go at milling the various splines I tried things out on a dummy piece.
here I am roughing out the splines for the sliding gear...

... and here I am cutting their sides.

Now I could round out the base circle between the splines in a series of cuts...

... after which the gear slid nicely on.

Similar procedure in cutting the splines for the fixed gears...

Only difference here is that you want the width of the splines correct to less than 1 thou, especially for the clutch. You'd really want to have a nice snug sliding fit without any shake!

I made a new layshaft as well, especially because the sliding gear and the kickstart gear were a pretty loose fit even on a NOS layshaft I had. Without boring you with any further small steps - here are the two shafts almost finished.

As mentioned before, I found all the gears having rather large running clearances on their respective part of the shafts - typically some 10 thou. I don't know if this is due to the wear and tear of the decades or if it was like this from new. If the latter, it is probably due to the fact that you could buy spares that needed to fit, taking all the manufacturing tolerances over the years into account. Or did Messrs Sturmey and Archer consider these large clearances necessary for the grease lubrocation of those days? Be that how it may, if precisely manufactured and running in oil, one thou should be just right.
So I made all the shafts to some 0.15mm oversize before hardening so I could then finish them to this clearance afterwards, having cleaned up the inside of the gears before.
Here I am just lapping the bore of the kickstart wheel to bring it back to round and cylindrical. If you happen to have a dismantled LS gearbox on your bench, and you have a good 3-point inside micrometer, measure the diameter at both ends and in the middle of the gear and I bet you will find it conical and trumpet shaped at the same time! I wonder how such a wobbling gear can work in practice, but apparently it does...?

While the shafts were away for case hardening I cleaned up the parts running on them. Here I clean up the bore in the sleeve gear. CBN inserts make a wonderful job of machining hardened steel these days, but they do not tolerate mistakes easily...

Still it is as well to make up a lap and lap the bore if you want it to be quite smooth.

Likewise I treated the bearing surfaces of the sliding gears, but it seems I have lost the pictures I have taken...
Now these are the bits back from case hardening. I had a crankpin treated at the same time, and a new chainwheel for the clutch.

All seemed well, but, unavoidably, the shafts had distorted a little during the heat treatment.
With +/- 0.08mm the runout was inside my final machining allowances for the bearing surfaces, but you want the splines to run true at the same time. So I had to figure out how to straighten the shafts.

I made a jig to to apply some brute force and tried to straighten the shafts cold. However, even bending the shafts by as much as 2.5 mm did not result in any permanent deformation - the shaft would just spring back into its original shape.
What finally did the trick was pre-tensioning the shaft by some 1.5mm and then putting a small point of heat with the oxacetylene torch on the side where the high spot was.

In the end I was able to reduce the runout to +/- .015mm - less than one thou.

Now the shafts could be machined to their final dimensions.
CBN inserts again - not all grades tolerate an interrupted cut as on the four splines for the sliding gears.

Again, a simple lapping ring is quickly made up and helps making a good finish and geometry.
I see I have not covered the lathe bed in doing so - shame on me! :-(

Finally, this is the complete gear cluster.
All the sections where hard steel runs in hard steel, i.e. the sliding gears on the shafts, the kickstart gear and the sleeve gear have now approx 0.03 to 0.04mm clearance. I hope this will be ok for oil lubrication.