AdamJ said:
Am I alone in finding lateral CA easier to correct in post than axial CA? I'd be happy to learn how to correct axial CA reliably.
Are you sure you have them the right way round?
http://www.cambridgeincolour.com/tutorials/lens-corrections.htm
The control panel in Lightroom-Develop-Lens Corrections-Color is all about correcting fringing, this can manifest from either lateral or axial CA. Though it can deal with blooming too, the colours are normally different. Lateral is two colours with red/magenta and green/yellow, axial is normally purple, as is blooming.
Just click the box! If that doesn't do the job very well adjusting the range and colour of the sliders will normally sort it out very well. You can even use the picker to select the exact tone of your problem CA/blooming.
Below are two images that illustrate dealing with lateral CA, the image is enlarged 200% and then a screen shot of the image and the control box.