Personally, I'd fit two separate controllers.
The complexity of having two machines wired into the same controller is just a headache waiting to happen.


As somebody who has retrofitted lathes and a milling machine, controller choice is more limited.
Last figures I seen, turn applications made up less than 10% of total user base, and I'd hazard to guess that has shrunk even further since I seen that figure, so it's not a high priority for developers.


If you really want to keep the same software for both, you're probably looking at Mach 3 or 4, LinuxCNC, Dynomotion KMotionCNC, or Centroid (there may be more, but those are the ones I know will support turning).



However my recommendation for a lathe now, is to go for a standalone Chinese controller, unless you really need conversational programming.
For a couple hundred pound, you can get a pretty good controller, without the expense of a PC/motion controller.

Milling machine, it's very much user preference.
I'd personally avoid the standalone Chinese controllers, as they are pretty limited memory wise (milling programs can run to many MBs - lathes you're lucky if you get to 10s of KBs, so can quickly run out of memory).
Again I'd consider if you need conversational. Conversational is good if you want to do a quick job like drill some holes, mill something flat, but if you're doing anything more complex, I find it far easier to just design the part in CAD/CAM.
Not having conversational, also opens up a lot more options for controllers/software.