What kind of lathe is it.
fwiw....bent shafts sometimes can be easily fixed by heating until it just begins to turn blue. Mount the shaft in v-blocks. Mount with high spot pointing upward. And locate the high spot pointing upward directly under a press. An arbor press would be ideal but I’ve used a hydraulic press on the last two I did.
So heat it till it’s blue. I used two small portable plumbing propane torches. Once it just discolors to a blue tinge....and we’re only aiming for the bent area to be blue, not the entire shaft. Use the press to then straighten the shaft.
FWIW....It seldom is going to come out perfect. But, what you will have is a fairly straight shaft. In your case, you’ll have a shaft in which will allow you to take measurements of the shaft.....then put the lathe back together.... and then use the lathe to make a replacement. It may come out good enough to forego making a replacement. I’ve had good luck doing a couple shafts like this. Now I’m not talking about large diameter shafts like the boat driveshafts Kieth Fenner straightens. I’m talking about shafts like you have there. About 1/2” diameter.