Good lighting is essential for lathe work. I really don’t think you can have too much. But general overhead lighting doesn’t cut it because you constantly need to train full, bright light on small details. I also use light to see the shape of my turnings not looking at the object itself, but using a shadow cast on a surface just behind the lathe. So close-up lighting for your lathe needs to be adjustable – and the more adjustable the better. I’m fond of reasonably inexpensive articulating arm lamps that are spring-tensioned. I use them around my lathe and on my bench.
Here in the Popular Woodworking Magazine shop I recently rigged up a fixture that mounts on our small Oneway lathe; it was amazingly easy to make, is quick to attach or remove and has multiple holes in which the lamp base can be placed for best positioning up and down the length of the lathe bed. On our lathe, there are metal brackets on top of the base behind the bed.