Yes I know what you are looking for I think - I was just saying that I have used the wizard and it works - at least in the version I have (I'll check which that one is).

OK, suppose you want a dome with a radius of curvature of 50 mm, so it's a "cap" sliced off a 100 mm dia sphere. This will be on the end of a 25mm diameter bar. In the OD Sphere wizard you set the sphere diameter to 100 mm and the Z centre position to -50 mm. X start is 25 and X end is 0 mm. Now you need to set Z end to the height of the dome. The distance of the dome centre to the centre of the bar end and to the dome edge will both be equal to its radius, but the edge will be set back from the bar centre by the height. If the sphere radius is R and the bar radius is r, then the height h is given by:

h = R - sqrt(R^2 - r^2)

where R^2 is "R squared".

For R = 50 and r = 12.5, h works out to 1.588 mm, so you put -1.588 for Zend.

The only problem with this for me is that it cuts edge to centre, with Z moving in a positive direction. My lathe has an ordinary Z leadscrew with significant backlash, and the cutting forces would be in the wrong direction. The X would be OK as it has a ballscrew. Really a better version would cut centre to edge. Anyway here's the G code the wizard generates.

G18 G64 G80 G90 G40 G49

M3

G00 X26.2

G00 Z0.6

F30

G00 Z-0.2577

G01 X25

G01 X25

G03 X22.8511 Z0 I-12.5 K-49.7423

G01 Z0.6

G00 X26.2

G00 Z-0.5155

G01 X25

G01 X25

G03 X20.4901 Z0 I-12.5 K-49.4845

G01 Z0.6

G00 X26.2

G00 Z-0.7734

G01 X25

G01 X25

G03 X17.833 Z0 I-12.5 K-49.2266

G01 Z0.6

G00 X26.2

G00 Z-1.0314

G01 X25

G01 X25

G03 X14.7204 Z0 I-12.5 K-48.9686

G01 Z0.6

G00 X26.2

G00 Z-1.2895

G01 X25

G01 X25

G03 X10.7639 Z0 I-12.5 K-48.7105

G01 Z0.6

G00 X26.2

G00 Z-1.4844

G01 X25

G01 X25

G03 X6.3277 Z0 I-12.5 K-48.5156

G01 Z0.6

G00 X26.2

F15

G00 Z-1.5877

G01 X25

G01 X24.9999

G03 X0 Z0 I-12.5 K-48.4123

G01 Z0.6

G00 X26.2

M5

M30

Having looked at this I realised that actually for my hemisphere I used the OD Fillet wizard for the above reason, but that only cuts full quarter circle fillets so won't work for you. Depending on your backlash you may be OK. Oh, and I think I have the same version as you - with the original one I used the wizard reliably crashed Mach 3.