Hi there,
It looks like the motor is hooked up as a shunt motor, which seems logical for application in a lathe-type device. The motor power is directly controlled using a rheostat in series with the arbor connection.
DC motors are torque champions at low speeds on directly driven applications. So if it is still good I would not retrofit the machine with an asynchronous AC motor and a VFD.
Check the DC resistance of the field winding between J and K. It should be around 600 ohms. The arbor should measure as a dead short or a few ohms, even as you turn the arbor. To really test the arbor you need to open up the brush compartment of the motor using the clips. Always do these measurments at power off! Put one probe on a a copper terminal of the arbor and leave it there. Work your way round with the other probe. You should measure almost a dead short between the copper terminals but the resistance will steadily increase as you get further away from the terminal where you left the first probe. always measure where the brushes are not wiping the arbor to avoid damage to the commutation bed. Are the brushes still OK?
Judging from the voltages on the name plate the machine is either 200V powered or has got a transformer or is powered directly of mains with a series resistor in the field winding to reduce field current at that higher mains voltage. You can use an of the shelve DC motor controller to control your motor. These low power ones usually have a directly rectified field output. So you need to use a series resistor in the field circuit to keep the current as close as possible to the specified 0,28A. The controller will also put a slightly higher voltage on the arbor but do not worry too much about that. You can limit the current to any amount you desire so the motor will not get overloaded. The simplest controllers accept a 0-10V speed signal, by means of a potmeter. Just put the controller in the cabinet, give it power, hook up the motor, drill a hole in the control panel for the potmeter, maybe a switch for forward and reverse and you are good to go. And if you really want to go all the way, you can attach a tacho generator to the shaft and thus have a speed feed-back to controller but that is up to you.
I am not affiliated with any brands but as an example, take the Parker 507.
Happy retrofitting!