Keep your eye on the calendar. Typically there is a lathe class or a mill class once a month and they alternate months. They are right before the Machine Shop committee meeting (which is usually the 4th Saturday of the month). Last month was mill so November will likely be lathe - although Thanksgiving may throw a wrench into that.
Also - be advised that each of those classes requires that you complete an online part 1 before you are eligible to sign up for the machine-side part 2.
Go to the Machine Shop talk category, and read ABOUT THIS CATEGORY, which has all the links, etc. for the prerequisite training.
Once the class posts to the calendar it will fill very quickly so I suggest you pre-emptively complete the online learning so you are eligible to register as soon as it opens.