The issue is with swtich start fluorescent lights, the ones with the little round "starter" in the side. Often they don't start instantly and may flicker on start.
They can flicker @ 50Hz, thus 3000 cycles per minute.
Now 3000 rpm is the synchronous speed for a 2 pole motor, however, with slip, which is needed the true speed will be nearer 2700-2960 rpm, depending on design & load, it will never reach synchronous speed, even off load.
It is very doubtful that your lathe will allow access to the running motor.
Thus the hazard is from the chuck/workpiece.
Check the speeds if they are fixed, and see how close you are to 50Hz/3000 rpm, and, even multiples & sub-multiples thereof.
If you have an HF light, which gives almost instantansous light, then the flicker frequency depends on the control gear, and is likely to be well away from any turning speed on a conventional metal cutting centre lathe.
Mind, if this is a new circuit, the electrical designer has a duty to have mitigated this, and if it is a new circuit, then you will have an EIC in accordance with BS7671 which will state that the design has been done in accordance with the requirements, so you have nothing to worry about, it's all been dealt with.
If it's not a new circuit, the people working on it should have been aware, and still mitigated any chance of this without you having to ask, else they are not competent.
HTH.