It would help others help you if the thread title related to the problem you have and if you told us a bit more about the lathe. Also what you have tried already.
My approach would be #1 spindle lock, #2 spin by hand, how does it feel, #3 slacken belt slightly, maybe it was too tight, #4 take belt off, see if motor starts now.
I'd also recall when it was last working, what's changed since? Did I change the belt onto a different pulley, open the cover, whatever. Is it the lathe or is it me? I has a minor panic recently only to realise I had laid a vacuum cleaner tube over the emergency stop button.
If it is one with electronic variable speed, think about the power supply. If it is via an extension lead, especially if there are other things running, you can get slight voltage drop at startup which can cause it to fail. My Coronet Herald was erratic until I realised and improved the layout and plugged directly into a socket.
Hope you get it working.