CNC machine lathes can run anywhere from $3000 for a small, mini-lathe upwards to tens of thousands of dollars.
Check out
www.grizzley.com www.harborfreight.com www.msc.com Do a google on cnc lathe or cnc mill and you'll find lots of wonderful sites. I have a mini-mill that I use for R/C parts, gun parts and some brackets and stuff. I also have many years of experience under my belt using machinery like that, it's not hard to learn, but it takes years to master and I'm far far away from mastery....
But, what you want to do is doable on a "regular" mini-lathe that Grizzley sells. If you take your time, you can even re-produce your joystick handles time and time again. Without having a CNC setup. I highly recommend digital Read Out's though... with that you'll be able to record exact measurements and follow them to the letter by hand, taking it slowly...
Mike B