I typically apply cutting oil by hand, and water soluble by a flood blast from a pump. (more or less)
Whenever I see a video of somebody using one of those old smaller turret lathes I watch. Slowly I've been piecing together everything I need to know to set up a job on mine.
Recently I watched a video and the operator was using pumped flood oil. It wasn't the blast of nozzles I use with water soluble coolant on the CNC mills, but it was a solid continuous stream.
I typically don't use flood on the lathe because I don't like being soaked by coolant, but this was controlled and the oil did not seem to be slung off like a water based cutting fluid. The other reason I don't often use flood on the lathe is the coolant evaporates just sitting there. I use my bigger lathe mostly for repair work. I use manually applied cutting fluids on the big manual mill for the same reason. The coolant disappears, even though I do use it a lot more than the lathe for roughing mold blanks to size. Neither gets used for many production jobs.
I'd like to hear your experiences and observations. If oil stays on the work better, and it doesn't evaporate (not at the same rate as water anyway) it could be an answer for lathe work.
I'd not have a problem dumping several gallons of relatively expensive cutting oil into the lathes (after cleaning them out) if it would reduce some of the headaches of cutting fluid on those machines. They both have tanks and pumps in their respective base. Maybe not the mill I use it at speeds and feeds that sling chips yards (meters), not inches (centimeters).