Generally the state of lathes "in their day" was that anyone who purchased a lathe sort of knew how to use it. There were exceptions. Certainly the Sears 109 lathes where Sears periodically published "project books" to educate unfamiliar buyers and entice those on the fence. Another exception would be the South Bend "How to Use a Lathe" books which featured exclusively South Bend products in the illustrations, but did have a higher calling to educating one to the capabilities of the machine they bought.
Actually, most lathes are *similar* in layout and function. As was typical of the trade, most lathe manufacturers tended to the familiar, and while different manufacturers might place the "half-nut" handle in a different place, the function remained the same - and most users could figure it out. Similarly for the rest of the lathe controls.
You may be where you "have to figure it out." Actually, the South Bend book might be a good place to start as South Bend lathes in their day were probably the MOST conventional of all. South Bend set both an operational and stylistic standard which others tended to emulate.
The book is online in many different places. Google "South Bend How to Run a Lathe." The books was (possibly IS) published over more than half a century in different editions differing little. One I picked up quickly at
http://vintagemachinery.org/pubs/1617/5795.pdf
Another book which you may benefit from might be Robert H. Smith's "Advanced Machine Work." Published in the early 20th century for probably 25 years first for use of MIT Engineering Students, later more generally. And not as advanced as he claims, the book is about half lathe, half other machine tools (to whet your appetite.) Found online at
http://www.opensourcemachinetools.org/archive-manuals/advanced-machine-work.pdf
Either of these books can be found in original hardcover from used booksellers for under $20, and new reprinted for only a little bit more.
We have more book suggestions than these, and are even available for specific queries. Welcome to the forum.
Joe in NH