Derry, looking at those photos I suspect that your lathe is based on the Hobbymat platform – it appears to have the cylindrical bed with a flat on the top. Also the locking screw on the tailstock barrel and the view into the headstock casing are suggestive. A 370 watt / .5 hp motor would surely be fine for this? The 1.1 kw you mention is drastic overkill!
If the Eurotherm controller is still OK I would stick with a DC motor. As there are 4 leads emerging from the present motor it is probably a wound-field type, but a modern PM motor would be perfectly fine. For example my Denford Novamill has a 375 W 5000 rpm PM motorwhich runs very quietly and has very smooth speed control. Modern controllers such as the Eurotherm have "IR compensation" which means that they give good speed control and high torque at low speeds. I found a data sheet for the type mentioned on the web which suggests that it does have an input for controlling externally from the CNC controller, even though that may not be connected at the moment. You would probably need a motor rated 375 watt with a running voltage of 180V max – this is what the Novamill motor has.
A few years ago I bought a DC servo motor and KB Electronics controller from Mr. Graham at Model Motors Direct – the controller now runs my Novamill but I have the motor which I have no plans for. It is rated 2A 110V – i.e. 220W or about 1/3 HP – as it is compatible with the KB controller it will run off the Eurotherm (though the latter would need a little adjustment, and you wouldn't need to use the field supply). PM or email me if you're interested – john.haine@ieee.org.
I used to have a Hobbymat, and I've converted my Super 7 to CNC and got my Novamill back from death's door which meant building all the electronics, happy to help if I can.
John.