I know the question of fluorescent lighting for rotating machinery has come up here before, general consensus has been it's not a real problem.
My 'new' lathe has an RS fluorescent worklight, with one of those 2D 'square' tubes in it. I've used it a number of times & there's been no problem.
Last night I changed the chuck, one 3-jaw for another, running at the same speed as before, & for a few moments I could have sworn that the spindle was running backwards. In fact I stopped it just to check which way it was going! Tried running it backwards, it was then less obvious which way it was 'running'. Curious that changing the chuck should change the perception. There was no way that I would have been fooled into thinking that it wasn't turning, even if the jaws has 'seemed' stationary.
Tim