Hey Hans,
sorry to hear that the controller board is messed up. You could try to contact other European suppliers that sell mini lathes (e.g. Holzmann, Paulimot, Optimum, HBM) and try to purchase a motor and controller board from them.
As I said earlier, you could also try for a sewing machine servo. As said earlier, in the German forum Zerspanungsbude are several threads for this type of motor.
Here is a thread where people adapted this type of servo to their machine. Imho, you will have to change the bolting pattern of the motor and the pulley in any case, unless you get a new original motor. To change the bore of the pulley you could turn the chuck by hand. It is not convenient, but it will do the job. For the keyway you could file that to the size needed, improvise this on your lathe (fix the chuck in place) or ask someone in your area to help you with that.
For the RPM-Range needed: Measure the pulley sizes you have right now. For my Holzmann ED300FD it was like "0" to 1250 and "0" to 2500, depending on the pulleys used. With that you can easily calculate how fast the motor must turn.
When I changed the motor for my lathe I turned 3 new pulleys to fit the speed range to my new motor (and the bigger V-belts). Luckily the old motor could be used for ~5 minutes before it got hot and had to cool down. If you want I can upload some photos of how I mounted the new motor. But it might be a few days before my little son lets me go to the workshop.