The simplest thing I can think of is a reflective optical switch (LED + PhotoTransistor in the same package) and a peice of black electrician's tape on a reflective spinning part of the lathe. Then all you have to do is count the number of pulses (1 per revolution) or time pulse length and display the result. A Microcontroller would probably be the easiest way to count pulses and display the result. You'll find tons of old posts about how to program the microcontroller and set up the opto switch.