One thing to be careful of is that some LED units have a strobing effect, while others shine continuously (I think this is more likely to be in an array of LEDs fed from AC rather than battery powered single LEDs). This has the ultimate problem when it can make something that is spinning appears to be stationary (very unlikely as they would have to be in sync) or at least give a weird effect that is off putting.
I have:
1) a clip-on LED from Woodart Products that uses a magnet to clip onto the back of the toolrest. This is brilliant when doing bowls. Highly recommended.
2) a halogen flood light pointed at the bed of the lathe. This is on all the time when working on it and the light colour is nice to work with (low temperature, warm). This is good and cheap.
3) a halogen spotlight that is dust proof from Axminster; this is good but bulky and so has been relegated to the bandsaw. The new ones they sell are LED based, so I don’t know if they are better.
4) an LED floodlight bought from Screwfix that I intended to use to replace the halogen (because the halogen is hot is use); this is the problem one with the strobe effect, so no longer used. Do not go this route.