You need at least three different oils, jonesy, for different jobs.
Firstly, for the ways (longitudinal and lateral slides) and screws you need a product the Americans call "way oil", which is a medium weight oil with a sticky additive. If you had a milling machine with a vertical slide, you'd need two grades of way oil: a normal one for the horizontal slides, and a heavy one for the vertical slide. A normal way oil doesn't stay in place on a vertical surface, it very slowly moves downward, so you use the heavy oil so it will take longer to get there. I've found I can't buy less than 20 litres of way oil through the trade, and I won't live long enough to use even 5 litres, so I cheat and use chainsaw bar oil. It has the same sticky additive as way oil, but it doesn't have a couple of other super-tricky additives to keep the slides from having a sort of slip-stick motion at ultra-slow feed speeds. I frankly doubt it makes any difference unless you are using a machine that has a hydraulic feed rather than a mechanical one.
The second kind of oil you need is for the spindle bearings. You put that in and forget it literally for several decades at a time. I'm assuming your lathe uses a roller bearing at the gear end, and a white-metal journal bearing with a thrust face, at the chuck end. If so the roller bearing will use grease, and the white-metal bearing will use a medium-weight liquid oil - it's best to read the lathe's manual to find out what they specify, and stick to that. Just be sure you keep the oil level at the line on the gauge glass there usually is on the front of the headstock. There are some lathes that use tapered roller bearings at both ends of the spindle, but that is frowned upon by lathe afficionados, on the grounds that you always end up with some spindle-lift if you do that, because of thermal expansion of the spindle, which causes changes in the end-float of the tapered rollers. Simple ballraces, of course, have a lot of radial slack and are never used even on cheap lathes. Mine has the usual one-roller-and-one-whitemetal arrangement, but it's 80 years old: they were all built that way then. I have the impression the cheap Chinese lathes use two roller bearings, but I haven't looked into it.
Third, you need an oil for gears, and for miscellaneous spindles etc. Some of these tend to have grease nipples, and on lathes, a grease nipple normally means you use grease, but keep in the back of your mind that milling machines commonly have grease nipples where you are supposed to use way oil, and other types of fitting where you use grease. Don't make the mistake I made when I first bought my mill, and blow a nylon lubrication line in an extremely inconvenient location, by trying to pump grease into the wrong place. To get back to the point, I use clean new automotive grade engine oil for those miscellaneous purposes, but if you have access to the manufacturer's manual, it will tell you what make and model of oil to use, and it may well be heavier than engine oil. You can probably find out what the recommended product actually consists of, by phoning a major oil company's technical advice service, and finding out what it is and what is an available alternative.
The important things to remember are, first, use way oil on slides and screws, and don't interchange oil and grease; and second, keep the machine lubricated. Clean and oil (with way oil) the leadscrew before you use it. Always clean down the slides when you finish a job, and ensure they end up still oily. Cover the machine when you aren't using it. Then apply fresh oil to the slides before use. Be careful to keep the scroll and jaw slides oiled in the self-centering chuck, and the screws and jaw slides in an independent jaw chuck. Don't let any oilable part of the machine get neglected - it is easy to forget one or two points, like the tailstock end of the feed shaft and the leadscrew, or maybe a couple of odd shafts in the headstock gears or the gears in the apron on the front of the carriage.
