It could be done but wont be just a straight swap, for a start your motors have resolvers and tachs which suggest that the drives (Amps ) will be analogue, that is no use for Mach. Rutex do a Step/Dir to analogue converter but so far I have not seen anyone that has used one. DSPMC do a motion controller that can control analogue drives and it seeminly works well but it is  fairly expensive. You will also have a lot of figuring out to do but as has been said you could convert but not just a case of plugging it in.
Hood

Sounds like my retrofit for my retrofit will cost more than I have in the whole lathe. Crap.

What current and voltage are your motors?
Hood

Pitman 19.1 VDC

that seems very low, was expecting 180 or 190V, what is the current of them? Or do you have a model number.
Hood

You are talking about the axis motors right?

yes, they are servo motors arent they?
Hood

This is the X axis motor. bad photo.

certainly look like dc servos, bit hard to tell from the pic, are there just two heavy wires to the motor itself? Any details or model numbers on the motor? What size is the lathe as the resolver size makes it look like the motor is fairly small.
Hood

Yes there are only 2 big wires. The motors are Pittman #13204C187 19.1 VDC. Attached is a photo of the lathe. It is a small one. Only 17" or so between centers.