Control system for Harrison M250 CNC

[m_c]

It all depends on how much functionality you want to add.

If you're happy with on screen jogging, and no fancy tool changer, Centroid Acorn will achieve that. If you want to add an MPG for jogging, then the Acorn is out (it only supports a single encoder input, and has limited inputs and outputs).
If you want more functionality, then a Dynomotion KFlop will give it, but it's not as easy a system to implement.

Mach is still an option, but being realistic for a lathe, you'd either have to ditch the spindle encoder and go single slot, or buy a motion controller that does support encoder threading with Mach. IIRC only the full fat CS-labs controllers with an additional MPG module support it, or a KFlop can work with encoders and Mach3. Some of the Galil controllers probably also support it, but I'm not sure on how well they work with Mach.

I think the CNC Drive UC controllers can support multi-slot threading, but not a full encoder. They also have their own control software, UCCNC, but I'm not sure how much support it has for lathes.
Out with that, you're into a bunch of controllers that can only support single slot threading, or controllers with no threading support. The best guesses I've seen for the number of turn/lathes users in the hobbyist/retrofit market, have all been less than 10%, so there just isn't the same level of support compared with mills/routers.

LinuxCNC with a Mesa card is another option.

Off course, the other option is a standalone controller.

It all comes down to how much money you're willing to spend, and what functionality you'd like.