Hi
In a previous life I trained/qualified as a sports fitness instructor/personal trainer and covered in depth the anatomy, physiology of the body, together with sports injuries.
The previous info given is as from what I can remember spot on. The pain will come from the trapisius muscle which is a complex muscle that runs on a triangle across your shoulders, up neck and down the mid section of your neck and back.
Tension is as said one of the main causes of stress within this muscle and can cause a lot of pain, but nothing serious if you do not let it carry on.
Your head is very heavy and if your lathe is set too low as stated you can for long periods of time be looking down more than needed which can cause stress on the central area of the muscle, so sitting at a computer in the wrong posture can also do it.
Raise the lathe to the correct height if not already done. It it is at the correct height make sure your posture is correct.
Your trapisius also raises/shrugs your shoulder so the basic fact of holding the tools and working will cause new movement in a way that you may have not done for some time. But you should only have stiffness in this situation and not great pain.
So look at your posture, how you hold your head and lathe set up.
The trapisius is a large muscle and in some cases a spasm in the uper neck can give you pain down in your buttocks, making you think that you have a lower back problem when in fact the problem is much higher up.