If these guys taught you how to run one, they are probably more knowledgeable about machines in general, and can educate you on what to look for. So many times I've seen beginners come to forums and ask questions about this stuff, only to be mislead by noobs ,hobbyists, amateurs and other inexperienced people just trying to be helpful. Seems like the blind is always willing to lead the blind nowadays. Stick with your mentors for hands on knowledge.
By the way, an "engine lathe" is old terminology. Engine lathes were powered by a steam engine, via a jack shaft. In today's world, they are known as "metal working lathes". Not to be a stickler, but the first step on the path to intelligence is to call things by their correct names. Knowing the nomenclature puts everyone on the same page, and makes things easier to learn.