+1 for Hoppers answer, with the caveat that older plain motor-oils are much closer to what's wanted than many modern motor oils. Over the years the latter have been highly modified to suit hot engines, cold-starts, engine efficiency and pollution control. Unfortunately the additives and formulation aren't good for lathes. You might have to look for plain motor oil, none of my local garages stock it. Last time I restocked with lawn-mower oil from a garden centre, but bigger car-places usually have plain motor oils on the shelf, and the internet is your friend.
The other thing to watch out for is gear-oil containing an additive that attacks copper – not good for bronze or brass components, if that's what your lathe has! Any gear oil marked 'Extreme' or with an E in the number is suspect, unfortunately some ordinary types have the same issue. Copper unsuitability is usually mentioned on the label, and always on the data-sheet.
As machines go, small lathes aren't particularly demanding on lubricants. Any oil is better than no oil. Perhaps the biggest boob is people using grease when oil is needed: Myford famously used grease nipples as oiling points, and a fair few owners jumped to the wrong conclusion, blocked their oil-ways with grease, and damaged the bearings…
Dave
Edited By SillyOldDuffer on 10/05/2019 10:19:33