I'm a machine builder by trade, and have literally looked over hundreds of used pieces of machinery in my lifetime. Have rebuilt a lot of machines in my lifetime as well. Mostly worked with machine centers, but as I see it, "it's all bearings, shafts, and gears."
* if the frame is cast iron, your ahead of the game from the start. Welded frames tend to flex all over the place, but this can easilly be delt with when the time comes.
* I'd look for something that has flame hardened ways on the frame, or at least removable ways.
* Look the machine over very closely in the area of the apron and compound. If the wipers are worn out, that should give you a hint as to how well the original owner took care of the machine. Expect the cross feed screw to show wear, but also check to see if the nut is out of adjustment. If it is, you'll need a new one
* expect the compound to show some wear. They should be rescraped about every 24 months of daily use. If it shows wear, be carefull who you have rescrape it!! If the wear shows at less than .002", it shouldn't take a guy much more than 16 hours to have it back to less than .0005". It it has much more, expect to either shim the backside of the gibs or buy new ones and do a complete rescrape (this can take as much as a week to get right.). Now is also a good time to set a parallel bar ontop of the compound (stone that face lightly for nicks and burrs). Then setup an indicator to see how parallel the mount is to the ways when you rotate it . Should come in at less than .0005".
* Now that we have the easy stuff out of the way, lets take a serious look at the apron. You need a couple of .0005" indicators (good ones) with mag bases. Set one up to read the longer ways that are part of the basic frame (we call that Z axis). Put one indicator on each side of the apron (in OTW one between the apron and the tail stock and the other on the opposite side. Crank the apron left and right a couple inches. The reading on the indicators will show the wear in the apron to the V and flat. It's going to have some, but hopefully it's under .00075". Now move the same indicators to the top of the ways and do the same thing. This should be well under .0005". If not it has to be rescraped, or maybe Mogliced. Now try to life the apron by hand. You still should be less than .001". Lastly with the half nut engage, check to see how much back lash it has in it when you try to crank the apron left to right. It will have some, but you don't want to see a bunch
Now lets look at the cross slide. This is where the wear really shows up in most lathes, but don't be too alarmed at what you see right away. Set the same pair of indicators up to read side movement, and crank the slide a couple inches. This should show less than .0015" in mid travel (never check anything at the furthest ends of travel by the way). Now crank the cross slide as far as you can away from you, and look at the condition of the ways. Look for deep scratches on the dovetails of the slide's ways. Look at them with a strong flashlight! Most of the time these will stone out, but will also get looser. Hopefully you can adjust this out with the gibs. I could take you much deeper into this, but the original owner might not like you pulling the gibs, or better yet pulling the complete crossslide (I always do). If he has not changed the wipers regularly there will be a lot of junk inside there, and that's not a good thing.
* Lets look over the tail stock. Set the same indicators up to check for wear. Expect the tail stock to change vertically when you clamp it down (supposed to). Now push the tail stock up close to the cross slide, and clamp it down. Run the quill out as far as you can. Set an indicator on top and on one side. It should be very strait, and run parallel with the ways when clamped down (I'm talking well under .0005"). But it probably won't. Now move the tail stock fairly close to the spindle, and set an indicator up to read the I.D. of the tailstock bore (where you will put a center in). It should read a couple tenths high if it's in good shape. Now put a dead center in it a read read it. The difference is the wear (or error machined in the quill I.D.). Now with the quill still clamped down in the tail stock; try to move it sideways and up and down. If you get movement you have a serious problem. I'd then recommend another machine as this is a very costly fix (I've done it, and don't recommend it fir the average Joe)
* now if you see a lot of junk in the ways, you can figure the samething in the chuck. Hopefully it has a scroll chuck or at least a good four jaw chuck. Chuck up a large gauge pin or ground down pin (drill rod will also work) that's about an inch in diameter. Check the run out (scroll chuck). Should be well under .001". Leave the indicator set up ontop of the pin (12 oclock), and take a three foot long wood 2x4, and try to pry the chuck upwards. Lets hope it's well under .00075", but don't be alarmed if it's .0015". Remove the chuck. If the owner says no, then look for another machine. With the chuck removed check the machine spindle for runout at 12 and 9 oclock. Most machine specs are under .0005" here.
Look at the very top of the head stock, and see if the bolts ontop have been messed with. If they have, you have had somebody inside the headstock. This can be OK and can be very bad. If the owner will allow you to remove the top plate, the try to pry the spindle forwards and backwards. A thousandth or more means the bearings need taken up (no big thing). Some lathes have clutches and some don't. Need to check them, but don't tighten them unless they are slipping. Now is the oil inside the cavity clean and clear? If it is that might mean that something was wrong prior to you looking in there. Clean and clear oil is always a bad sign when looking over machinery. But it should not very very dirty as well. You'll know what looks right.
I'd also check the pulleys for wear from the belts, and make sure they are tight on the motor and spindle. If they show signs of wrenched take a serious look at them This can be an expensive fis is the shafts are worn.
If the head stock is not cast into the frame, then you might have to realign the head stock. Not a big deal after you've done it a few times, but also not for amatures.
+++++++++++++++++++++++++++++++++++++++++++++++++++++++
here's what I usually take with me to look over a used lathe
* a 1" diameter piece of Thompson rod or drill rod that I know is strait. @4" long is about right. If you can get your hands on the tubular Thompson rod you way ahead of the game by the way
* two very good quality .0005" wand type indicators with mag bases
* a three foot long 2x4
* a set of Allen wrenches and a hand full of screw drivers (be sure to bring two with large heads for gibs that are about 3/8" wide. I usually bring a foot long piece of 1/2" black pipe to use as a cheater on the allen wrenches
* a couple precision levels would be nice, but you can get a rough idea with good torpedo levels
* a 12" long parallel bar that's at least 1/2" wide and 2" tall
* a good bright flashlight
* one set of feeler gauges are very handy to see how loose the gibs are
gary