That will be a really solid built and rugged lathe. Most things I'd be looking at are not really Monarch specific, but just how I'd approach any machine.
First and foremost way condition. Next I'd love to look inside headstock if that option were available, but may not be. If you can look in headstock, just be careful with the weight of top cover. It could be easy to drop as they are heavy and awkward.
Pretty good idea to shift all the speeds on head stock. Listen to each gear running after engaged. Notice your engagement how it pops or locks in. Shift all the speeds on qcgb. Run the controls on apron etc.
Look up inside qcgb at the gears. How does clutch engagement feel ? Does tail stock move in and out nice, and how's its taper ? Maybe lift up and down on handwheels and dials. How's the electrical system look.
Even with a nice machine, I'm going to find something. It just a fact of life, if its 50 to 80 years old there will be something. Just need to decide to live with it, or address and fix it. The higher the cost on machine the more picky I'd get. If its cheap, just buy it and quit messing around
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If you're in Illinois, then you have more options for shopping around and getting decent prices.
And don't let the lube system thread bother you, for the most part that's not Monarch specific either. Any old machine that uses bijur metering units will have some or even most not working. One way or another you have to deal with them. or use a paint brush to lube your machine if need be
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On leveling, the bases and bed are structurally pretty rigid. Dont let 8 adjusting points drive you crazy. Even with using a .0005" level it can go pretty quick, but because the bed and bases are pretty rigid you'd have to wait a few weeks after initial leveling for it to settle a bit. You'll find any two of 4 bolts on a base will very easy jack the other two bolts in the air. So basically get level with 2 bolts on each base, then bring the other two bolts down to get a little tension on them, without jacking the other two up.