Your local chapter(s) are a great place to ask. Ours has complete lathe setups we loan to new turners; someone among the membership almost always has a lathe available over the course of a few months as they upgrade equipment.
Craigslist and FB marketplace are the next obvious sources. In our area there are always a half dozen interesting lathes for sale at any given time. They are simple machines, not much to go wrong and not much that's hard to fix if it does. It's rare to find a lathe that has been worn out. Replacing belts and bearings is pretty easy. You should be able to tell if the motor is working, on a belt driven machine swapping the motor out is typically trivial. A lathe with a dead motor may be an advantage as used three phase motors are typically cheap, and in combination with a VFD can add variable speed readily to an older lathe. Avoid models that have odd spindle and taper sizes, if you stick to #2 morse tapers and one of the common spindle threads like 1-1/4 x 8 tpi then any of your accessories like chucks will transfer when you decide to upgrade.
There are, of course a million new choices. In general the same dollars will get you a much nicer piece of equipment used than new.