What was produced when the lathe was produced was just a very basic oil. Even straight mineral oil would be pretty comparable. While you're welcome to do something more advanced, like a Mobil DTE with anti-wear additives, the cheap stuff from the tractor supply is unquestionably sufficient for the construction and speeds of your lathe and the rate of use of even a particularly active hobbyist.
I should mention that the manual also says to use "a small amount of graphite grease" on the apron and leadscrew gears. I like "engine assembly lube" because, at least in the form I bought on a clearance rack a few years ago, it is a squeeze tube of graphite-molybdenum grease. I just squeeze a little out onto a couple gears then run the gears for 10-20 seconds each way about once every week or two. No need to get my finger or anything else all greasy that way.